diff --git a/xarray/tests/test_cupy.py b/xarray/tests/test_cupy.py
new file mode 100644
index 00000000000..624e78d9271
--- /dev/null
+++ b/xarray/tests/test_cupy.py
@@ -0,0 +1,50 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+import xarray as xr
+
+cp = pytest.importorskip("cupy")
+
+
+@pytest.fixture
+def toy_weather_data():
+    """Construct the example DataSet from the Toy weather data example.
+
+    http://xarray.pydata.org/en/stable/examples/weather-data.html
+
+    Here we construct the DataSet exactly as shown in the example and then
+    convert the numpy arrays to cupy.
+
+    """
+    np.random.seed(123)
+    times = pd.date_range("2000-01-01", "2001-12-31", name="time")
+    annual_cycle = np.sin(2 * np.pi * (times.dayofyear.values / 365.25 - 0.28))
+
+    base = 10 + 15 * annual_cycle.reshape(-1, 1)
+    tmin_values = base + 3 * np.random.randn(annual_cycle.size, 3)
+    tmax_values = base + 10 + 3 * np.random.randn(annual_cycle.size, 3)
+
+    ds = xr.Dataset(
+        {
+            "tmin": (("time", "location"), tmin_values),
+            "tmax": (("time", "location"), tmax_values),
+        },
+        {"time": times, "location": ["IA", "IN", "IL"]},
+    )
+
+    ds.tmax.data = cp.asarray(ds.tmax.data)
+    ds.tmin.data = cp.asarray(ds.tmin.data)
+
+    return ds
+
+
+def test_cupy_import():
+    """Check the import worked."""
+    assert cp
+
+
+def test_check_data_stays_on_gpu(toy_weather_data):
+    """Perform some operations and check the data stays on the GPU."""
+    freeze = (toy_weather_data["tmin"] <= 0).groupby("time.month").mean("time")
+    assert isinstance(freeze.data, cp.core.core.ndarray)