diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index b3130a1a4ab..38f183f9fc2 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -55,6 +55,8 @@ Enhancements
 Bug fixes
 ~~~~~~~~~
 
+- Fixed ``decode_cf`` function to operate lazily on dask arrays
+  (:issue:`1372`). By `Ryan Abernathey <https://github.com/rabernat>`_.
 - Fixed labeled indexing with slice bounds given by xarray objects with
   datetime64 or timedelta64 dtypes (:issue:`1240`).
   By `Stephan Hoyer <https://github.com/shoyer>`_.
diff --git a/xarray/conventions.py b/xarray/conventions.py
index 93fd56ed5d2..04664435732 100644
--- a/xarray/conventions.py
+++ b/xarray/conventions.py
@@ -9,7 +9,7 @@
 from .coding import times, variables
 from .coding.variables import SerializationWarning
 from .core import duck_array_ops, indexing
-from .core.pycompat import OrderedDict, basestring, iteritems
+from .core.pycompat import OrderedDict, basestring, iteritems, dask_array_type
 from .core.variable import IndexVariable, Variable, as_variable
 
 
@@ -490,8 +490,9 @@ def decode_cf_variable(name, var, concat_characters=True, mask_and_scale=True,
         del attributes['dtype']
         data = BoolTypeArray(data)
 
-    return Variable(dimensions, indexing.LazilyOuterIndexedArray(data),
-                    attributes, encoding=encoding)
+    if not isinstance(data, dask_array_type):
+        data = indexing.LazilyOuterIndexedArray(data)
+    return Variable(dimensions, data, attributes, encoding=encoding)
 
 
 def decode_cf_variables(variables, attributes, concat_characters=True,
diff --git a/xarray/tests/test_conventions.py b/xarray/tests/test_conventions.py
index 5b82f5a26f2..86240f4e33e 100644
--- a/xarray/tests/test_conventions.py
+++ b/xarray/tests/test_conventions.py
@@ -18,7 +18,7 @@
 
 from . import (
     IndexerMaker, TestCase, assert_array_equal, raises_regex, requires_netCDF4,
-    requires_netcdftime, unittest)
+    requires_netcdftime, unittest, requires_dask)
 from .test_backends import CFEncodedDataTest
 
 B = IndexerMaker(indexing.BasicIndexer)
@@ -332,6 +332,17 @@ def test_decode_cf_datetime_transition_to_invalid(self):
 
         assert_array_equal(ds_decoded.time.values, expected)
 
+    @requires_dask
+    def test_decode_cf_with_dask(self):
+        import dask
+        original = Dataset({
+            't': ('t', [0, 1, 2], {'units': 'days since 2000-01-01'}),
+            'foo': ('t', [0, 0, 0], {'coordinates': 'y', 'units': 'bar'}),
+            'y': ('t', [5, 10, -999], {'_FillValue': -999})
+        }).chunk({'t': 1})
+        decoded = conventions.decode_cf(original)
+        assert dask.is_dask_collection(decoded.y.data)
+
 
 class CFEncodedInMemoryStore(WritableCFDataStore, InMemoryDataStore):
     pass