diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index eda5c9dfbf6..0a9a1464df1 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -96,7 +96,7 @@ Documentation
 Internal Changes
 ~~~~~~~~~~~~~~~~
 - Use :py:func:`dask.array.apply_gufunc` instead of :py:func:`dask.array.blockwise` in
-  :py:func:`xarray.apply_ufunc` when using ``dask='parallelized'``. (:pull:`4060`, :pull:`4391`)
+  :py:func:`xarray.apply_ufunc` when using ``dask='parallelized'``. (:pull:`4060`, :pull:`4391`, :pull:`4392`)
 - Fix ``pip install .`` when no ``.git`` directory exists; namely when the xarray source
   directory has been rsync'ed by PyCharm Professional for a remote deployment over SSH.
   By `Guido Imperiale <https://github.com/crusaderky>`_
diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index 507f12fe55e..db4a9b46e98 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -625,6 +625,26 @@ def apply_variable_ufunc(
             if dask_gufunc_kwargs is None:
                 dask_gufunc_kwargs = {}
 
+            allow_rechunk = dask_gufunc_kwargs.get("allow_rechunk", None)
+            if allow_rechunk is None:
+                for n, (data, core_dims) in enumerate(
+                    zip(input_data, signature.input_core_dims)
+                ):
+                    if is_duck_dask_array(data):
+                        # core dimensions cannot span multiple chunks
+                        for axis, dim in enumerate(core_dims, start=-len(core_dims)):
+                            if len(data.chunks[axis]) != 1:
+                                raise ValueError(
+                                    f"dimension {dim} on {n}th function argument to "
+                                    "apply_ufunc with dask='parallelized' consists of "
+                                    "multiple chunks, but is also a core dimension. To "
+                                    "fix, either rechunk into a single dask array chunk along "
+                                    f"this dimension, i.e., ``.chunk({dim}: -1)``, or "
+                                    "pass ``allow_rechunk=True`` in ``dask_gufunc_kwargs`` "
+                                    "but beware that this may significantly increase memory usage."
+                                )
+                dask_gufunc_kwargs["allow_rechunk"] = True
+
             output_sizes = dask_gufunc_kwargs.pop("output_sizes", {})
             if output_sizes:
                 output_sizes_renamed = {}
diff --git a/xarray/tests/test_computation.py b/xarray/tests/test_computation.py
index 7cb755b6dac..63bedfaf280 100644
--- a/xarray/tests/test_computation.py
+++ b/xarray/tests/test_computation.py
@@ -695,8 +695,7 @@ def check(x, y):
     check(data_array, 0 * data_array)
     check(data_array, 0 * data_array[0])
     check(data_array[:, 0], 0 * data_array[0])
-    with raises_regex(ValueError, "with different chunksize present"):
-        check(data_array, 0 * data_array.compute())
+    check(data_array, 0 * data_array.compute())
 
 
 @requires_dask
@@ -710,7 +709,7 @@ def test_apply_dask_parallelized_errors():
     with raises_regex(ValueError, "at least one input is an xarray object"):
         apply_ufunc(identity, array, dask="parallelized")
 
-    # formerly from _apply_blockwise, now from dask.array.apply_gufunc
+    # formerly from _apply_blockwise, now from apply_variable_ufunc
     with raises_regex(ValueError, "consists of multiple chunks"):
         apply_ufunc(
             identity,