diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index e62c7e87d44..3fdb6b4ae82 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -63,6 +63,10 @@ Enhancements
 Bug fixes
 ~~~~~~~~~
 
+- Rolling operations on xarray objects containing dask arrays could silently
+  compute the incorrect result or use large amounts of memory (:issue:`2940`).
+  For now, these operations have been disabled with an explicit error.
+  By `Stephan Hoyer <https://github.com/shoyer>`_.
 - NetCDF4 output: variables with unlimited dimensions must be chunked (not
   contiguous) on output. (:issue:`1849`)
   By `James McCreight <https://github.com/jmccreight>`_.
diff --git a/xarray/core/dask_array_ops.py b/xarray/core/dask_array_ops.py
index 7e72c93da27..7e1b898f437 100644
--- a/xarray/core/dask_array_ops.py
+++ b/xarray/core/dask_array_ops.py
@@ -20,6 +20,13 @@
 
 def dask_rolling_wrapper(moving_func, a, window, min_count=None, axis=-1):
     '''wrapper to apply bottleneck moving window funcs on dask arrays'''
+
+    raise NotImplementedError(
+        'rolling operations on xarray objects backed by dask arrays have not '
+        'been implemented yet (https://github.com/pydata/xarray/issues/2940). '
+        'For now, load your arrays into memory for rolling window operations '
+        'by calling .compute().')
+
     dtype, fill_value = dtypes.maybe_promote(a.dtype)
     a = a.astype(dtype)
     # inputs for overlap
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index fd9076e7f65..c8bfa65b7d5 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -3724,9 +3724,16 @@ def test_rolling_wrapped_dask_nochunk(center):
 
     da_day_clim = xr.DataArray(np.arange(1, 367),
                                coords=[np.arange(1, 367)], dims='dayofyear')
-    expected = da_day_clim.rolling(dayofyear=31, center=center).mean()
-    actual = da_day_clim.chunk().rolling(dayofyear=31, center=center).mean()
-    assert_allclose(actual, expected)
+    expected = da_day_clim.rolling(dayofyear=31, center=center).mean()  # noqa
+    actual = da_day_clim.chunk().rolling(  # noqa
+        dayofyear=31, center=center).mean()
+    print(actual)
+    with pytest.raises(NotImplementedError):
+        actual = da_day_clim.chunk().rolling(  # noqa
+            dayofyear=31, center=center).mean()
+    # TODO: uncomment this assertion once we fix rolling window operations with
+    # dask (https://github.com/pydata/xarray/issues/2940)
+    # assert_allclose(actual, expected)
 
 
 @pytest.mark.parametrize('center', (True, False))