diff --git a/cubed/overlap.py b/cubed/overlap.py
index d93c2b89..8ae2785c 100644
--- a/cubed/overlap.py
+++ b/cubed/overlap.py
@@ -134,6 +134,6 @@ def _pad_boundaries(x, depth, boundary, numblocks, block_id):
         p = nxp.full_like(x, fill_value=boundary[i], shape=pad_shape)
         if block_id[i] == 0:  # first block on axis i
             x = nxp.concat([p, x], axis=i)
-        elif block_id[i] == numblocks[i] - 1:  # last block on axis i
+        if block_id[i] == numblocks[i] - 1:  # last block on axis i
             x = nxp.concat([x, p], axis=i)
     return x
diff --git a/cubed/tests/test_overlap.py b/cubed/tests/test_overlap.py
index 0d8e3a18..5c29e3a7 100644
--- a/cubed/tests/test_overlap.py
+++ b/cubed/tests/test_overlap.py
@@ -22,6 +22,23 @@ def test_map_overlap_1d():
     assert_array_equal(b.compute(), np.array([0, 0, 1, 2, 3, 2, 3, 4, 5, 0]))
 
 
+def test_map_overlap_1d_single_chunk():
+    x = np.arange(6)
+    a = xp.asarray(x, chunks=(6,))
+
+    b = cubed.map_overlap(
+        lambda x: x,
+        a,
+        dtype=a.dtype,
+        chunks=((8,),),
+        depth=1,
+        boundary=0,
+        trim=False,
+    )
+
+    assert_array_equal(b.compute(), np.array([0, 0, 1, 2, 3, 4, 5, 0]))
+
+
 def test_map_overlap_2d():
     x = np.arange(36).reshape((6, 6))
     a = xp.asarray(x, chunks=(3, 3))