diff --git a/Lib/SimpleXMLRPCServer.py b/Lib/SimpleXMLRPCServer.py
index 6af2f2f..23ad5bd 100644
--- a/Lib/SimpleXMLRPCServer.py
+++ b/Lib/SimpleXMLRPCServer.py
@@ -459,7 +459,10 @@
             L = []
             while size_remaining:
                 chunk_size = min(size_remaining, max_chunk_size)
-                L.append(self.rfile.read(chunk_size))
+                chunk = self.rfile.read(chunk_size)
+                if not chunk:
+                    break
+                L.append(chunk)
                 size_remaining -= len(L[-1])
             data = ''.join(L)