diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 47bc8719c35..c185fbd49eb 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -417,7 +417,13 @@ class _Stream:
             self.fileobj.write(self.buf)
             self.buf = ""
             if self.comptype == "gz":
-                self.fileobj.write(struct.pack("<l", self.crc))
+                # The native zlib crc is an unsigned 32-bit integer, but
+                # the Python wrapper implicitly casts that to a signed C
+                # long.  So, on a 32-bit box self.crc may "look negative",
+                # while the same crc on a 64-bit box may "look positive".
+                # To avoid irksome warnings from the `struct` module, force
+                # it to look positive on all boxes.
+                self.fileobj.write(struct.pack("<L", self.crc & 0xffffffffL))
                 self.fileobj.write(struct.pack("<L", self.pos & 0xffffFFFFL))
 
         if not self._extfileobj: