diff --git a/s3fs/core.py b/s3fs/core.py
index f3dc411d..9b9a3f57 100644
--- a/s3fs/core.py
+++ b/s3fs/core.py
@@ -1275,17 +1275,14 @@ async def _upload_chunk(chunk, part_number):
                     chunks.append(chunk)
             if not chunks:
                 break
-            if len(chunks) > 1:
-                out.extend(
-                    await asyncio.gather(
-                        *[
-                            _upload_chunk(chunk, len(out) + i)
-                            for i, chunk in enumerate(chunks, 1)
-                        ]
-                    )
+            out.extend(
+                await asyncio.gather(
+                    *[
+                        _upload_chunk(chunk, len(out) + i)
+                        for i, chunk in enumerate(chunks, 1)
+                    ]
                 )
-            else:
-                out.append(await _upload_chunk(chunk, len(out) + 1))
+            )
         return out
 
     async def _get_file(
diff --git a/s3fs/tests/test_s3fs.py b/s3fs/tests/test_s3fs.py
index 3379da52..b64907d1 100644
--- a/s3fs/tests/test_s3fs.py
+++ b/s3fs/tests/test_s3fs.py
@@ -1017,6 +1017,24 @@ def test_put_file_with_callback(s3, tmpdir, size):
     assert cb.size == os.stat(test_file).st_size
     assert cb.value == cb.size
 
+    assert s3.size(test_bucket_name + "/temp") == 11 * size
+
+
+@pytest.mark.parametrize("factor", [1, 5, 6])
+def test_put_file_does_not_truncate(s3, tmpdir, factor):
+    test_file = str(tmpdir.join("test.json"))
+
+    chunksize = 5 * 2**20
+    block = b"x" * chunksize
+
+    with open(test_file, "wb") as f:
+        f.write(block * factor)
+
+    s3.put_file(
+        test_file, test_bucket_name + "/temp", max_concurrency=5, chunksize=chunksize
+    )
+    assert s3.size(test_bucket_name + "/temp") == factor * chunksize
+
 
 @pytest.mark.parametrize("size", [2**10, 2**20, 10 * 2**20])
 def test_pipe_cat_big(s3, size):