diff --git a/xarray/tests/test_dask.py b/xarray/tests/test_dask.py
index d5d460056aa..fa49d253e26 100644
--- a/xarray/tests/test_dask.py
+++ b/xarray/tests/test_dask.py
@@ -104,6 +104,11 @@ def test_chunk(self):
             assert rechunked.chunks == expected
             self.assertLazyAndIdentical(self.eager_var, rechunked)
 
+            expected_chunksizes = {
+                dim: chunks for dim, chunks in zip(self.lazy_var.dims, expected)
+            }
+            assert rechunked.chunksizes == expected_chunksizes
+
     def test_indexing(self):
         u = self.eager_var
         v = self.lazy_var
@@ -330,6 +335,38 @@ def setUp(self):
             self.data, coords={"x": range(4)}, dims=("x", "y"), name="foo"
         )
 
+    def test_chunk(self):
+        for chunks, expected in [
+            ({}, ((2, 2), (2, 2, 2))),
+            (3, ((3, 1), (3, 3))),
+            ({"x": 3, "y": 3}, ((3, 1), (3, 3))),
+            ({"x": 3}, ((3, 1), (2, 2, 2))),
+            ({"x": (3, 1)}, ((3, 1), (2, 2, 2))),
+        ]:
+            # Test DataArray
+            rechunked = self.lazy_array.chunk(chunks)
+            assert rechunked.chunks == expected
+            self.assertLazyAndIdentical(self.eager_array, rechunked)
+
+            expected_chunksizes = {
+                dim: chunks for dim, chunks in zip(self.lazy_array.dims, expected)
+            }
+            assert rechunked.chunksizes == expected_chunksizes
+
+            # Test Dataset
+            lazy_dataset = self.lazy_array.to_dataset()
+            eager_dataset = self.eager_array.to_dataset()
+            expected_chunksizes = {
+                dim: chunks for dim, chunks in zip(lazy_dataset.dims, expected)
+            }
+            rechunked = lazy_dataset.chunk(chunks)
+
+            # Dataset.chunks has a different return type to DataArray.chunks - see issue #5843
+            assert rechunked.chunks == expected_chunksizes
+            self.assertLazyAndIdentical(eager_dataset, rechunked)
+
+            assert rechunked.chunksizes == expected_chunksizes
+
     def test_rechunk(self):
         chunked = self.eager_array.chunk({"x": 2}).chunk({"y": 2})
         assert chunked.chunks == ((2,) * 2, (2,) * 3)