diff --git a/tornado/platform/asyncio.py b/tornado/platform/asyncio.py
index b7b63d199..fc20661bd 100644
--- a/tornado/platform/asyncio.py
+++ b/tornado/platform/asyncio.py
@@ -52,6 +52,8 @@
 class _HasFileno(Protocol):
     def fileno(self) -> int:
         pass
+    def __hash__(self) -> int:
+        pass
 
 
 _FileDescriptorLike = Union[int, _HasFileno]