diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 27709a09e7a..d07872a9364 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -32,6 +32,8 @@ Bug fixes
   By `Mayeul d'Avezac <https://github.com/mdavezac>`_.
 - Return correct count for scalar datetime64 arrays (:issue:`2770`)
   By `Dan Nowacki <https://github.com/dnowacki-usgs>`_.
+- A deep copy deep-copies the coords (:issue:`1463`)
+  By `Martin Pletcher <https://github.com/pletchm>`_.
 
 .. _whats-new.0.12.1:
 
diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index 96c6b7bd59b..41f8795b595 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -1906,7 +1906,8 @@ def copy(self, deep=True, data=None):
         Parameters
         ----------
         deep : bool, optional
-            Deep is always ignored.
+            Deep is ignored when data is given. Whether the data array is
+            loaded into memory and copied onto the new object. Default is True.
         data : array_like, optional
             Data to use in the new object. Must have same shape as original.
 
@@ -1917,7 +1918,14 @@ def copy(self, deep=True, data=None):
             data copied from original.
         """
         if data is None:
-            data = self._data
+            if deep:
+                # self._data should be a `PandasIndexAdapter` instance at this
+                # point, which doesn't have a copy method, so make a deep copy
+                # of the underlying `pandas.MultiIndex` and create a new
+                # `PandasIndexAdapter` instance with it.
+                data = PandasIndexAdapter(self._data.array.copy(deep=True))
+            else:
+                data = self._data
         else:
             data = as_compatible_data(data)
             if self.shape != data.shape:
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 58eb6a1d6dc..6084368d8a1 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -3297,6 +3297,28 @@ def test_copy_with_data(self):
         expected.data = new_data
         assert_identical(expected, actual)
 
+    @pytest.mark.parametrize('deep, expected_orig', [
+        [True,
+         xr.DataArray(xr.IndexVariable('a', np.array([1, 2])),
+                      coords={'a': [1, 2]}, dims=['a'])],
+        [False,
+         xr.DataArray(xr.IndexVariable('a', np.array([999, 2])),
+                      coords={'a': [999, 2]}, dims=['a'])]])
+    def test_copy_coords(self, deep, expected_orig):
+        da = xr.DataArray(
+            np.ones([2, 2, 2]),
+            coords={'a': [1, 2], 'b': ['x', 'y'], 'c': [0, 1]},
+            dims=['a', 'b', 'c'])
+        da_cp = da.copy(deep)
+        da_cp['a'].data[0] = 999
+
+        expected_cp = xr.DataArray(
+            xr.IndexVariable('a', np.array([999, 2])),
+            coords={'a': [999, 2]}, dims=['a'])
+        assert_identical(da_cp['a'], expected_cp)
+
+        assert_identical(da['a'], expected_orig)
+
     def test_real_and_imag(self):
         array = DataArray(1 + 2j)
         assert_identical(array.real, DataArray(1))
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 3ace80f5eea..b98c0509754 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -1923,6 +1923,29 @@ def test_copy_with_data(self):
             expected[k].data = v
         assert_identical(expected, actual)
 
+    @pytest.mark.parametrize('deep, expected_orig', [
+        [True,
+         xr.DataArray(xr.IndexVariable('a', np.array([1, 2])),
+                      coords={'a': [1, 2]}, dims=['a'])],
+        [False,
+         xr.DataArray(xr.IndexVariable('a', np.array([999, 2])),
+                      coords={'a': [999, 2]}, dims=['a'])]])
+    def test_copy_coords(self, deep, expected_orig):
+        ds = xr.DataArray(
+            np.ones([2, 2, 2]),
+            coords={'a': [1, 2], 'b': ['x', 'y'], 'c': [0, 1]},
+            dims=['a', 'b', 'c'],
+            name='value').to_dataset()
+        ds_cp = ds.copy(deep=deep)
+        ds_cp.coords['a'].data[0] = 999
+
+        expected_cp = xr.DataArray(
+            xr.IndexVariable('a', np.array([999, 2])),
+            coords={'a': [999, 2]}, dims=['a'])
+        assert_identical(ds_cp.coords['a'], expected_cp)
+
+        assert_identical(ds.coords['a'], expected_orig)
+
     def test_copy_with_data_errors(self):
         orig = create_test_data()
         new_var1 = np.arange(orig['var1'].size).reshape(orig['var1'].shape)