diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index ac80524a3c4..86272cf8710 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -43,6 +43,8 @@ New Features
   arguments and should instead pass a single list of dimensions.
   (:pull:`3802`)
   By `Maximilian Roos <https://github.com/max-sixty>`_
+- :py:func:`map_blocks` can now apply functions that add new unindexed dimensions.
+  By `Deepak Cherian <https://github.com/dcherian>`_
 - The new ``Dataset._repr_html_`` and ``DataArray._repr_html_`` (introduced
   in 0.14.1) is now on by default. To disable, use
   ``xarray.set_options(display_style="text")``.
@@ -60,7 +62,6 @@ New Features
   (:issue:`3843`, :pull:`3844`) 
   By `Aaron Spring <https://github.com/aaronspring>`_.
 
-
 Bug fixes
 ~~~~~~~~~
 - Fix :py:meth:`Dataset.interp` when indexing array shares coordinates with the
diff --git a/xarray/core/parallel.py b/xarray/core/parallel.py
index 8429d0f71ad..6f1668f698f 100644
--- a/xarray/core/parallel.py
+++ b/xarray/core/parallel.py
@@ -386,6 +386,9 @@ def _wrapper(func, obj, to_array, args, kwargs):
                 var_chunks.append(input_chunks[dim])
             elif dim in indexes:
                 var_chunks.append((len(indexes[dim]),))
+            elif dim in template.dims:
+                # new unindexed dimension
+                var_chunks.append((template.sizes[dim],))
 
         data = dask.array.Array(
             hlg, name=gname_l, chunks=var_chunks, dtype=template[name].dtype
diff --git a/xarray/tests/test_dask.py b/xarray/tests/test_dask.py
index 4f7e3910f82..923b35e5946 100644
--- a/xarray/tests/test_dask.py
+++ b/xarray/tests/test_dask.py
@@ -1147,6 +1147,7 @@ def test_map_blocks_to_array(map_ds):
         lambda x: x.to_dataset(),
         lambda x: x.drop_vars("x"),
         lambda x: x.expand_dims(k=[1, 2, 3]),
+        lambda x: x.expand_dims(k=3),
         lambda x: x.assign_coords(new_coord=("y", x.y * 2)),
         lambda x: x.astype(np.int32),
         # TODO: [lambda x: x.isel(x=1).drop_vars("x"), map_da],
@@ -1167,6 +1168,7 @@ def test_map_blocks_da_transformations(func, map_da):
         lambda x: x.drop_vars("a"),
         lambda x: x.drop_vars("x"),
         lambda x: x.expand_dims(k=[1, 2, 3]),
+        lambda x: x.expand_dims(k=3),
         lambda x: x.rename({"a": "new1", "b": "new2"}),
         # TODO: [lambda x: x.isel(x=1)],
     ],