diff --git a/src/libstd/sync/mpsc/mod.rs b/src/libstd/sync/mpsc/mod.rs
index 059ced4f56e..99424c8a92f 100644
--- a/src/libstd/sync/mpsc/mod.rs
+++ b/src/libstd/sync/mpsc/mod.rs
@@ -1321,12 +1321,13 @@ impl<T> Receiver<T> {
         // Do an optimistic try_recv to avoid the performance impact of
         // Instant::now() in the full-channel case.
         match self.try_recv() {
-            Ok(result)
-                => Ok(result),
-            Err(TryRecvError::Disconnected)
-                => Err(RecvTimeoutError::Disconnected),
-            Err(TryRecvError::Empty)
-                => self.recv_deadline(Instant::now() + timeout)
+            Ok(result) => Ok(result),
+            Err(TryRecvError::Disconnected) => Err(RecvTimeoutError::Disconnected),
+            Err(TryRecvError::Empty) => match Instant::now().checked_add(timeout) {
+                Some(deadline) => self.recv_deadline(deadline),
+                // So far in the future that it's practically the same as waiting indefinitely.
+                None => self.recv().map_err(RecvTimeoutError::from),
+            },
         }
     }
 
@@ -2311,6 +2312,17 @@ mod tests {
         assert_eq!(recv_count, stress);
     }
 
+    #[test]
+    fn very_long_recv_timeout_wont_panic() {
+        let (tx, rx) = channel::<()>();
+        let join_handle = thread::spawn(move || {
+            rx.recv_timeout(Duration::from_secs(u64::max_value()))
+        });
+        thread::sleep(Duration::from_secs(1));
+        assert!(tx.send(()).is_ok());
+        assert_eq!(join_handle.join().unwrap(), Ok(()));
+    }
+
     #[test]
     fn recv_a_lot() {
         // Regression test that we don't run out of stack in scheduler context