diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 8303113600b..670ee021107 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -36,6 +36,8 @@ Deprecations
 Bug fixes
 ~~~~~~~~~
 
+- Fix bug with rechunking to a frequency when some periods contain no data (:issue:`9360`).
+  By `Deepak Cherian <https://github.com/dcherian>`_.
 - Fix bug causing `DataTree.from_dict` to be sensitive to insertion order (:issue:`9276`, :pull:`9292`).
   By `Tom Nicholas <https://github.com/TomNicholas>`_.
 - Fix resampling error with monthly, quarterly, or yearly frequencies with
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 62183adcf71..628a2efa61e 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2752,7 +2752,7 @@ def _resolve_frequency(
                 )
 
             assert variable.ndim == 1
-            chunks: tuple[int, ...] = tuple(
+            chunks = (
                 DataArray(
                     np.ones(variable.shape, dtype=int),
                     dims=(name,),
@@ -2760,9 +2760,13 @@ def _resolve_frequency(
                 )
                 .resample({name: resampler})
                 .sum()
-                .data.tolist()
             )
-            return chunks
+            # When bins (binning) or time periods are missing (resampling)
+            # we can end up with NaNs. Drop them.
+            if chunks.dtype.kind == "f":
+                chunks = chunks.dropna(name).astype(int)
+            chunks_tuple: tuple[int, ...] = tuple(chunks.data.tolist())
+            return chunks_tuple
 
         chunks_mapping_ints: Mapping[Any, T_ChunkDim] = {
             name: (
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index f859ff38ccb..a43e3d15e32 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -1209,24 +1209,34 @@ def get_dask_names(ds):
         ),
     )
     @pytest.mark.parametrize("freq", ["D", "W", "5ME", "YE"])
-    def test_chunk_by_frequency(self, freq, calendar) -> None:
+    @pytest.mark.parametrize("add_gap", [True, False])
+    def test_chunk_by_frequency(self, freq: str, calendar: str, add_gap: bool) -> None:
         import dask.array
 
         N = 365 * 2
+        ΔN = 28
+        time = xr.date_range(
+            "2001-01-01", periods=N + ΔN, freq="D", calendar=calendar
+        ).to_numpy()
+        if add_gap:
+            # introduce an empty bin
+            time[31 : 31 + ΔN] = np.datetime64("NaT")
+            time = time[~np.isnat(time)]
+        else:
+            time = time[:N]
+
         ds = Dataset(
             {
                 "pr": ("time", dask.array.random.random((N), chunks=(20))),
                 "pr2d": (("x", "time"), dask.array.random.random((10, N), chunks=(20))),
                 "ones": ("time", np.ones((N,))),
             },
-            coords={
-                "time": xr.date_range(
-                    "2001-01-01", periods=N, freq="D", calendar=calendar
-                )
-            },
+            coords={"time": time},
         )
         rechunked = ds.chunk(x=2, time=TimeResampler(freq))
-        expected = tuple(ds.ones.resample(time=freq).sum().data.tolist())
+        expected = tuple(
+            ds.ones.resample(time=freq).sum().dropna("time").astype(int).data.tolist()
+        )
         assert rechunked.chunksizes["time"] == expected
         assert rechunked.chunksizes["x"] == (2,) * 5