diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 4497c57e5f2..918106a45df 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -123,6 +123,10 @@ Bug fixes
   By `Spencer Clark <https://github.com/spencerkclark>`_.
 - Avoid use of Dask's deprecated ``get=`` parameter in tests
   by `Matthew Rocklin <https://github.com/mrocklin/>`_.
+- An ``OverflowError`` is now accurately raised and caught during the
+  encoding process if a reference date is used that is so distant that
+  the dates must be encoded using cftime rather than NumPy (:issue:`2272`).
+  By `Spencer Clark <https://github.com/spencerkclark>`_.
 
 .. _whats-new.0.10.9:
 
diff --git a/xarray/coding/times.py b/xarray/coding/times.py
index dff7e75bdcf..16380976def 100644
--- a/xarray/coding/times.py
+++ b/xarray/coding/times.py
@@ -361,7 +361,12 @@ def encode_cf_datetime(dates, units=None, calendar=None):
         delta_units = _netcdf_to_numpy_timeunit(delta)
         time_delta = np.timedelta64(1, delta_units).astype('timedelta64[ns]')
         ref_date = np.datetime64(pd.Timestamp(ref_date))
-        num = (dates - ref_date) / time_delta
+
+        # Wrap the dates in a DatetimeIndex to do the subtraction to ensure
+        # an OverflowError is raised if the ref_date is too far away from
+        # dates to be encoded (GH 2272).
+        num = (pd.DatetimeIndex(dates.ravel()) - ref_date) / time_delta
+        num = num.values.reshape(dates.shape)
 
     except (OutOfBoundsDatetime, OverflowError):
         num = _encode_datetime_with_cftime(dates, units, calendar)
diff --git a/xarray/tests/test_coding_times.py b/xarray/tests/test_coding_times.py
index 10a1a956b27..8e47bd37eac 100644
--- a/xarray/tests/test_coding_times.py
+++ b/xarray/tests/test_coding_times.py
@@ -8,7 +8,8 @@
 import pytest
 
 from xarray import DataArray, Variable, coding, decode_cf, set_options
-from xarray.coding.times import _import_cftime
+from xarray.coding.times import (_import_cftime, decode_cf_datetime,
+                                 encode_cf_datetime)
 from xarray.coding.variables import SerializationWarning
 from xarray.core.common import contains_cftime_datetimes
 
@@ -763,3 +764,16 @@ def test_contains_cftime_datetimes_non_cftimes(non_cftime_data):
 @pytest.mark.parametrize('non_cftime_data', [DataArray([]), DataArray([1, 2])])
 def test_contains_cftime_datetimes_non_cftimes_dask(non_cftime_data):
     assert not contains_cftime_datetimes(non_cftime_data.chunk())
+
+
+@pytest.mark.skipif(not has_cftime_or_netCDF4, reason='cftime not installed')
+@pytest.mark.parametrize('shape', [(24,), (8, 3), (2, 4, 3)])
+def test_encode_datetime_overflow(shape):
+    # Test for fix to GH 2272
+    dates = pd.date_range('2100', periods=24).values.reshape(shape)
+    units = 'days since 1800-01-01'
+    calendar = 'standard'
+
+    num, _, _ = encode_cf_datetime(dates, units, calendar)
+    roundtrip = decode_cf_datetime(num, units, calendar)
+    np.testing.assert_array_equal(dates, roundtrip)