diff --git a/src/pipe/chunked.rs b/src/pipe/chunked.rs
index b60dbb1..5d34597 100644
--- a/src/pipe/chunked.rs
+++ b/src/pipe/chunked.rs
@@ -148,6 +148,13 @@ pub(crate) struct Writer {
 
 impl AsyncWrite for Writer {
     fn poll_write(mut self: Pin<&mut Self>, cx: &mut Context<'_>, buf: &[u8]) -> Poll<io::Result<usize>> {
+        // If the pipe is closed then return prematurely, otherwise we'd be
+        // spending time writing the entire buffer only to discover that it is
+        // closed afterward.
+        if self.buf_stream_tx.is_closed() {
+            return Poll::Ready(Err(io::ErrorKind::BrokenPipe.into()));
+        }
+
         // Attempt to grab an available buffer to write the chunk to.
         match self.buf_pool_rx.poll_next_unpin(cx) {
             // Wait for the reader to finish reading a chunk.
@@ -221,4 +228,19 @@ mod tests {
             assert_eq!(reader.read(&mut dest).await.unwrap(), 0);
         })
     }
+
+    #[test]
+    fn writer_errors_if_reader_is_dropped() {
+        let waker = noop_waker();
+        let mut context = Context::from_waker(&waker);
+
+        let (mut reader, mut writer) = new(2);
+
+        drop(reader);
+
+        match writer.write(b"hello").poll_unpin(&mut context) {
+            Poll::Ready(Err(e)) => assert_eq!(e.kind(), io::ErrorKind::BrokenPipe),
+            _ => panic!("expected poll to be ready"),
+        }
+    }
 }