diff --git a/src/librustc_parse/parser/diagnostics.rs b/src/librustc_parse/parser/diagnostics.rs
index 9abfbc698c5cf..ecbd183b6e929 100644
--- a/src/librustc_parse/parser/diagnostics.rs
+++ b/src/librustc_parse/parser/diagnostics.rs
@@ -4,6 +4,7 @@ use rustc_data_structures::fx::FxHashSet;
 use rustc_error_codes::*;
 use rustc_errors::{pluralize, struct_span_err};
 use rustc_errors::{Applicability, DiagnosticBuilder, Handler, PResult};
+use rustc_span::source_map::Spanned;
 use rustc_span::symbol::kw;
 use rustc_span::{MultiSpan, Span, SpanSnippetError, DUMMY_SP};
 use syntax::ast::{
@@ -500,6 +501,58 @@ impl<'a> Parser<'a> {
         }
     }
 
+    /// Check to see if a pair of chained operators looks like an attempt at chained comparison,
+    /// e.g. `1 < x <= 3`. If so, suggest either splitting the comparison into two, or
+    /// parenthesising the leftmost comparison.
+    fn attempt_chained_comparison_suggestion(
+        &mut self,
+        err: &mut DiagnosticBuilder<'_>,
+        inner_op: &Expr,
+        outer_op: &Spanned<AssocOp>,
+    ) {
+        if let ExprKind::Binary(op, ref l1, ref r1) = inner_op.kind {
+            match (op.node, &outer_op.node) {
+                // `x < y < z` and friends.
+                (BinOpKind::Lt, AssocOp::Less) | (BinOpKind::Lt, AssocOp::LessEqual) |
+                (BinOpKind::Le, AssocOp::LessEqual) | (BinOpKind::Le, AssocOp::Less) |
+                // `x > y > z` and friends.
+                (BinOpKind::Gt, AssocOp::Greater) | (BinOpKind::Gt, AssocOp::GreaterEqual) |
+                (BinOpKind::Ge, AssocOp::GreaterEqual) | (BinOpKind::Ge, AssocOp::Greater) => {
+                    let expr_to_str = |e: &Expr| {
+                        self.span_to_snippet(e.span)
+                            .unwrap_or_else(|_| pprust::expr_to_string(&e))
+                    };
+                    err.span_suggestion(
+                        inner_op.span.to(outer_op.span),
+                        "split the comparison into two...",
+                        format!(
+                            "{} {} {} && {} {}",
+                            expr_to_str(&l1),
+                            op.node.to_string(),
+                            expr_to_str(&r1),
+                            expr_to_str(&r1),
+                            outer_op.node.to_ast_binop().unwrap().to_string(),
+                        ),
+                        Applicability::MaybeIncorrect,
+                    );
+                    err.span_suggestion(
+                        inner_op.span.to(outer_op.span),
+                        "...or parenthesize one of the comparisons",
+                        format!(
+                            "({} {} {}) {}",
+                            expr_to_str(&l1),
+                            op.node.to_string(),
+                            expr_to_str(&r1),
+                            outer_op.node.to_ast_binop().unwrap().to_string(),
+                        ),
+                        Applicability::MaybeIncorrect,
+                    );
+                }
+                _ => {}
+            }
+        }
+    }
+
     /// Produces an error if comparison operators are chained (RFC #558).
     /// We only need to check the LHS, not the RHS, because all comparison ops have same
     /// precedence (see `fn precedence`) and are left-associative (see `fn fixity`).
@@ -515,27 +568,31 @@ impl<'a> Parser<'a> {
     ///           /   \
     ///     inner_op   r2
     ///        /  \
-    ///     l1    r1
+    ///      l1    r1
     pub(super) fn check_no_chained_comparison(
         &mut self,
-        lhs: &Expr,
-        outer_op: &AssocOp,
+        inner_op: &Expr,
+        outer_op: &Spanned<AssocOp>,
     ) -> PResult<'a, Option<P<Expr>>> {
         debug_assert!(
-            outer_op.is_comparison(),
+            outer_op.node.is_comparison(),
             "check_no_chained_comparison: {:?} is not comparison",
-            outer_op,
+            outer_op.node,
         );
 
         let mk_err_expr =
             |this: &Self, span| Ok(Some(this.mk_expr(span, ExprKind::Err, AttrVec::new())));
 
-        match lhs.kind {
+        match inner_op.kind {
             ExprKind::Binary(op, _, _) if op.node.is_comparison() => {
                 // Respan to include both operators.
                 let op_span = op.span.to(self.prev_span);
-                let mut err = self
-                    .struct_span_err(op_span, "chained comparison operators require parentheses");
+                let mut err =
+                    self.struct_span_err(op_span, "comparison operators cannot be chained");
+
+                // If it looks like a genuine attempt to chain operators (as opposed to a
+                // misformatted turbofish, for instance), suggest a correct form.
+                self.attempt_chained_comparison_suggestion(&mut err, inner_op, outer_op);
 
                 let suggest = |err: &mut DiagnosticBuilder<'_>| {
                     err.span_suggestion_verbose(
@@ -547,12 +604,12 @@ impl<'a> Parser<'a> {
                 };
 
                 if op.node == BinOpKind::Lt &&
-                    *outer_op == AssocOp::Less ||  // Include `<` to provide this recommendation
-                    *outer_op == AssocOp::Greater
+                    outer_op.node == AssocOp::Less ||  // Include `<` to provide this recommendation
+                    outer_op.node == AssocOp::Greater
                 // even in a case like the following:
                 {
                     //     Foo<Bar<Baz<Qux, ()>>>
-                    if *outer_op == AssocOp::Less {
+                    if outer_op.node == AssocOp::Less {
                         let snapshot = self.clone();
                         self.bump();
                         // So far we have parsed `foo<bar<`, consume the rest of the type args.
@@ -584,7 +641,7 @@ impl<'a> Parser<'a> {
                                 // FIXME: actually check that the two expressions in the binop are
                                 // paths and resynthesize new fn call expression instead of using
                                 // `ExprKind::Err` placeholder.
-                                mk_err_expr(self, lhs.span.to(self.prev_span))
+                                mk_err_expr(self, inner_op.span.to(self.prev_span))
                             }
                             Err(mut expr_err) => {
                                 expr_err.cancel();
@@ -606,7 +663,7 @@ impl<'a> Parser<'a> {
                                 // FIXME: actually check that the two expressions in the binop are
                                 // paths and resynthesize new fn call expression instead of using
                                 // `ExprKind::Err` placeholder.
-                                mk_err_expr(self, lhs.span.to(self.prev_span))
+                                mk_err_expr(self, inner_op.span.to(self.prev_span))
                             }
                         }
                     } else {
diff --git a/src/librustc_parse/parser/expr.rs b/src/librustc_parse/parser/expr.rs
index 90f15375aec42..3c286d363c9db 100644
--- a/src/librustc_parse/parser/expr.rs
+++ b/src/librustc_parse/parser/expr.rs
@@ -5,7 +5,7 @@ use super::{SemiColonMode, SeqSep, TokenExpectType};
 use crate::maybe_recover_from_interpolated_ty_qpath;
 
 use rustc_errors::{Applicability, PResult};
-use rustc_span::source_map::{self, Span};
+use rustc_span::source_map::{self, Span, Spanned};
 use rustc_span::symbol::{kw, sym, Symbol};
 use std::mem;
 use syntax::ast::{self, AttrStyle, AttrVec, CaptureBy, Field, Ident, Lit, DUMMY_NODE_ID};
@@ -181,17 +181,17 @@ impl<'a> Parser<'a> {
             };
 
             let cur_op_span = self.token.span;
-            let restrictions = if op.is_assign_like() {
+            let restrictions = if op.node.is_assign_like() {
                 self.restrictions & Restrictions::NO_STRUCT_LITERAL
             } else {
                 self.restrictions
             };
-            let prec = op.precedence();
+            let prec = op.node.precedence();
             if prec < min_prec {
                 break;
             }
             // Check for deprecated `...` syntax
-            if self.token == token::DotDotDot && op == AssocOp::DotDotEq {
+            if self.token == token::DotDotDot && op.node == AssocOp::DotDotEq {
                 self.err_dotdotdot_syntax(self.token.span);
             }
 
@@ -200,11 +200,12 @@ impl<'a> Parser<'a> {
             }
 
             self.bump();
-            if op.is_comparison() {
+            if op.node.is_comparison() {
                 if let Some(expr) = self.check_no_chained_comparison(&lhs, &op)? {
                     return Ok(expr);
                 }
             }
+            let op = op.node;
             // Special cases:
             if op == AssocOp::As {
                 lhs = self.parse_assoc_op_cast(lhs, lhs_span, ExprKind::Cast)?;
@@ -298,7 +299,7 @@ impl<'a> Parser<'a> {
     }
 
     fn should_continue_as_assoc_expr(&mut self, lhs: &Expr) -> bool {
-        match (self.expr_is_complete(lhs), self.check_assoc_op()) {
+        match (self.expr_is_complete(lhs), self.check_assoc_op().map(|op| op.node)) {
             // Semi-statement forms are odd:
             // See https://github.com/rust-lang/rust/issues/29071
             (true, None) => false,
@@ -343,19 +344,22 @@ impl<'a> Parser<'a> {
     /// The method does not advance the current token.
     ///
     /// Also performs recovery for `and` / `or` which are mistaken for `&&` and `||` respectively.
-    fn check_assoc_op(&self) -> Option<AssocOp> {
-        match (AssocOp::from_token(&self.token), &self.token.kind) {
-            (op @ Some(_), _) => op,
-            (None, token::Ident(sym::and, false)) => {
-                self.error_bad_logical_op("and", "&&", "conjunction");
-                Some(AssocOp::LAnd)
-            }
-            (None, token::Ident(sym::or, false)) => {
-                self.error_bad_logical_op("or", "||", "disjunction");
-                Some(AssocOp::LOr)
-            }
-            _ => None,
-        }
+    fn check_assoc_op(&self) -> Option<Spanned<AssocOp>> {
+        Some(Spanned {
+            node: match (AssocOp::from_token(&self.token), &self.token.kind) {
+                (Some(op), _) => op,
+                (None, token::Ident(sym::and, false)) => {
+                    self.error_bad_logical_op("and", "&&", "conjunction");
+                    AssocOp::LAnd
+                }
+                (None, token::Ident(sym::or, false)) => {
+                    self.error_bad_logical_op("or", "||", "disjunction");
+                    AssocOp::LOr
+                }
+                _ => return None,
+            },
+            span: self.token.span,
+        })
     }
 
     /// Error on `and` and `or` suggesting `&&` and `||` respectively.
diff --git a/src/test/ui/did_you_mean/issue-40396.rs b/src/test/ui/did_you_mean/issue-40396.rs
index 1893355205433..e4e94bb949237 100644
--- a/src/test/ui/did_you_mean/issue-40396.rs
+++ b/src/test/ui/did_you_mean/issue-40396.rs
@@ -1,8 +1,8 @@
 fn main() {
     (0..13).collect<Vec<i32>>();
-    //~^ ERROR chained comparison
+    //~^ ERROR comparison operators cannot be chained
     Vec<i32>::new();
-    //~^ ERROR chained comparison
+    //~^ ERROR comparison operators cannot be chained
     (0..13).collect<Vec<i32>();
-    //~^ ERROR chained comparison
+    //~^ ERROR comparison operators cannot be chained
 }
diff --git a/src/test/ui/did_you_mean/issue-40396.stderr b/src/test/ui/did_you_mean/issue-40396.stderr
index 749d1093ccab8..f952136a7bfe3 100644
--- a/src/test/ui/did_you_mean/issue-40396.stderr
+++ b/src/test/ui/did_you_mean/issue-40396.stderr
@@ -1,15 +1,23 @@
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/issue-40396.rs:2:20
    |
 LL |     (0..13).collect<Vec<i32>>();
    |                    ^^^^^
    |
+help: split the comparison into two...
+   |
+LL |     (0..13).collect < Vec && Vec <i32>>();
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     ((0..13).collect < Vec) <i32>>();
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^
 help: use `::<...>` instead of `<...>` to specify type arguments
    |
 LL |     (0..13).collect::<Vec<i32>>();
    |                    ^^
 
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/issue-40396.rs:4:8
    |
 LL |     Vec<i32>::new();
@@ -20,12 +28,20 @@ help: use `::<...>` instead of `<...>` to specify type arguments
 LL |     Vec::<i32>::new();
    |        ^^
 
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/issue-40396.rs:6:20
    |
 LL |     (0..13).collect<Vec<i32>();
    |                    ^^^^^
    |
+help: split the comparison into two...
+   |
+LL |     (0..13).collect < Vec && Vec <i32>();
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     ((0..13).collect < Vec) <i32>();
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^
 help: use `::<...>` instead of `<...>` to specify type arguments
    |
 LL |     (0..13).collect::<Vec<i32>();
diff --git a/src/test/ui/parser/chained-comparison-suggestion.rs b/src/test/ui/parser/chained-comparison-suggestion.rs
new file mode 100644
index 0000000000000..0431196f1744e
--- /dev/null
+++ b/src/test/ui/parser/chained-comparison-suggestion.rs
@@ -0,0 +1,40 @@
+// Check that we get nice suggestions when attempting a chained comparison.
+
+fn comp1() {
+    1 < 2 <= 3; //~ ERROR comparison operators cannot be chained
+    //~^ ERROR mismatched types
+}
+
+fn comp2() {
+    1 < 2 < 3; //~ ERROR comparison operators cannot be chained
+}
+
+fn comp3() {
+    1 <= 2 < 3; //~ ERROR comparison operators cannot be chained
+    //~^ ERROR mismatched types
+}
+
+fn comp4() {
+    1 <= 2 <= 3; //~ ERROR comparison operators cannot be chained
+    //~^ ERROR mismatched types
+}
+
+fn comp5() {
+    1 > 2 >= 3; //~ ERROR comparison operators cannot be chained
+    //~^ ERROR mismatched types
+}
+
+fn comp6() {
+    1 > 2 > 3; //~ ERROR comparison operators cannot be chained
+}
+
+fn comp7() {
+    1 >= 2 > 3; //~ ERROR comparison operators cannot be chained
+}
+
+fn comp8() {
+    1 >= 2 >= 3; //~ ERROR comparison operators cannot be chained
+    //~^ ERROR mismatched types
+}
+
+fn main() {}
diff --git a/src/test/ui/parser/chained-comparison-suggestion.stderr b/src/test/ui/parser/chained-comparison-suggestion.stderr
new file mode 100644
index 0000000000000..5c10a4599dd03
--- /dev/null
+++ b/src/test/ui/parser/chained-comparison-suggestion.stderr
@@ -0,0 +1,159 @@
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:4:7
+   |
+LL |     1 < 2 <= 3;
+   |       ^^^^^^
+   |
+help: split the comparison into two...
+   |
+LL |     1 < 2 && 2 <= 3;
+   |     ^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 < 2) <= 3;
+   |     ^^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:9:7
+   |
+LL |     1 < 2 < 3;
+   |       ^^^^^
+   |
+   = help: use `::<...>` instead of `<...>` to specify type arguments
+   = help: or use `(...)` if you meant to specify fn arguments
+help: split the comparison into two...
+   |
+LL |     1 < 2 && 2 < 3;
+   |     ^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 < 2) < 3;
+   |     ^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:13:7
+   |
+LL |     1 <= 2 < 3;
+   |       ^^^^^^
+   |
+help: split the comparison into two...
+   |
+LL |     1 <= 2 && 2 < 3;
+   |     ^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 <= 2) < 3;
+   |     ^^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:18:7
+   |
+LL |     1 <= 2 <= 3;
+   |       ^^^^^^^
+   |
+help: split the comparison into two...
+   |
+LL |     1 <= 2 && 2 <= 3;
+   |     ^^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 <= 2) <= 3;
+   |     ^^^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:23:7
+   |
+LL |     1 > 2 >= 3;
+   |       ^^^^^^
+   |
+help: split the comparison into two...
+   |
+LL |     1 > 2 && 2 >= 3;
+   |     ^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 > 2) >= 3;
+   |     ^^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:28:7
+   |
+LL |     1 > 2 > 3;
+   |       ^^^^^
+   |
+   = help: use `::<...>` instead of `<...>` to specify type arguments
+   = help: or use `(...)` if you meant to specify fn arguments
+help: split the comparison into two...
+   |
+LL |     1 > 2 && 2 > 3;
+   |     ^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 > 2) > 3;
+   |     ^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:32:7
+   |
+LL |     1 >= 2 > 3;
+   |       ^^^^^^
+   |
+   = help: use `::<...>` instead of `<...>` to specify type arguments
+   = help: or use `(...)` if you meant to specify fn arguments
+help: split the comparison into two...
+   |
+LL |     1 >= 2 && 2 > 3;
+   |     ^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 >= 2) > 3;
+   |     ^^^^^^^^^^
+
+error: comparison operators cannot be chained
+  --> $DIR/chained-comparison-suggestion.rs:36:7
+   |
+LL |     1 >= 2 >= 3;
+   |       ^^^^^^^
+   |
+help: split the comparison into two...
+   |
+LL |     1 >= 2 && 2 >= 3;
+   |     ^^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (1 >= 2) >= 3;
+   |     ^^^^^^^^^^^
+
+error[E0308]: mismatched types
+  --> $DIR/chained-comparison-suggestion.rs:4:14
+   |
+LL |     1 < 2 <= 3;
+   |              ^ expected `bool`, found integer
+
+error[E0308]: mismatched types
+  --> $DIR/chained-comparison-suggestion.rs:13:14
+   |
+LL |     1 <= 2 < 3;
+   |              ^ expected `bool`, found integer
+
+error[E0308]: mismatched types
+  --> $DIR/chained-comparison-suggestion.rs:18:15
+   |
+LL |     1 <= 2 <= 3;
+   |               ^ expected `bool`, found integer
+
+error[E0308]: mismatched types
+  --> $DIR/chained-comparison-suggestion.rs:23:14
+   |
+LL |     1 > 2 >= 3;
+   |              ^ expected `bool`, found integer
+
+error[E0308]: mismatched types
+  --> $DIR/chained-comparison-suggestion.rs:36:15
+   |
+LL |     1 >= 2 >= 3;
+   |               ^ expected `bool`, found integer
+
+error: aborting due to 13 previous errors
+
+For more information about this error, try `rustc --explain E0308`.
diff --git a/src/test/ui/parser/require-parens-for-chained-comparison.rs b/src/test/ui/parser/require-parens-for-chained-comparison.rs
index 9c7a25d589a1f..e27b03dddc5be 100644
--- a/src/test/ui/parser/require-parens-for-chained-comparison.rs
+++ b/src/test/ui/parser/require-parens-for-chained-comparison.rs
@@ -3,24 +3,26 @@ struct X;
 
 fn main() {
     false == false == false;
-    //~^ ERROR chained comparison operators require parentheses
+    //~^ ERROR comparison operators cannot be chained
 
     false == 0 < 2;
-    //~^ ERROR chained comparison operators require parentheses
+    //~^ ERROR comparison operators cannot be chained
     //~| ERROR mismatched types
     //~| ERROR mismatched types
 
     f<X>();
-    //~^ ERROR chained comparison operators require parentheses
+    //~^ ERROR comparison operators cannot be chained
     //~| HELP use `::<...>` instead of `<...>` to specify type arguments
 
     f<Result<Option<X>, Option<Option<X>>>(1, 2);
-    //~^ ERROR chained comparison operators require parentheses
+    //~^ ERROR comparison operators cannot be chained
+    //~| HELP split the comparison into two...
+    //~| ...or parenthesize one of the comparisons
     //~| HELP use `::<...>` instead of `<...>` to specify type arguments
 
     use std::convert::identity;
     let _ = identity<u8>;
-    //~^ ERROR chained comparison operators require parentheses
+    //~^ ERROR comparison operators cannot be chained
     //~| HELP use `::<...>` instead of `<...>` to specify type arguments
     //~| HELP or use `(...)` if you meant to specify fn arguments
 }
diff --git a/src/test/ui/parser/require-parens-for-chained-comparison.stderr b/src/test/ui/parser/require-parens-for-chained-comparison.stderr
index bece9a388008c..44edf2de7f8de 100644
--- a/src/test/ui/parser/require-parens-for-chained-comparison.stderr
+++ b/src/test/ui/parser/require-parens-for-chained-comparison.stderr
@@ -1,16 +1,16 @@
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/require-parens-for-chained-comparison.rs:5:11
    |
 LL |     false == false == false;
    |           ^^^^^^^^^^^
 
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/require-parens-for-chained-comparison.rs:8:11
    |
 LL |     false == 0 < 2;
    |           ^^^^^^
 
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/require-parens-for-chained-comparison.rs:13:6
    |
 LL |     f<X>();
@@ -21,19 +21,27 @@ help: use `::<...>` instead of `<...>` to specify type arguments
 LL |     f::<X>();
    |      ^^
 
-error: chained comparison operators require parentheses
+error: comparison operators cannot be chained
   --> $DIR/require-parens-for-chained-comparison.rs:17:6
    |
 LL |     f<Result<Option<X>, Option<Option<X>>>(1, 2);
    |      ^^^^^^^^
    |
+help: split the comparison into two...
+   |
+LL |     f < Result && Result <Option<X>, Option<Option<X>>>(1, 2);
+   |     ^^^^^^^^^^^^^^^^^^^^^^
+help: ...or parenthesize one of the comparisons
+   |
+LL |     (f < Result) <Option<X>, Option<Option<X>>>(1, 2);
+   |     ^^^^^^^^^^^^^^
 help: use `::<...>` instead of `<...>` to specify type arguments
    |
 LL |     f::<Result<Option<X>, Option<Option<X>>>(1, 2);
    |      ^^
 
-error: chained comparison operators require parentheses
-  --> $DIR/require-parens-for-chained-comparison.rs:22:21
+error: comparison operators cannot be chained
+  --> $DIR/require-parens-for-chained-comparison.rs:24:21
    |
 LL |     let _ = identity<u8>;
    |                     ^^^^