diff --git a/tokio-stream/src/stream_ext/chunks_timeout.rs b/tokio-stream/src/stream_ext/chunks_timeout.rs
index 107101317a3..48acd9328bc 100644
--- a/tokio-stream/src/stream_ext/chunks_timeout.rs
+++ b/tokio-stream/src/stream_ext/chunks_timeout.rs
@@ -1,6 +1,6 @@
 use crate::stream_ext::Fuse;
 use crate::Stream;
-use tokio::time::{sleep, Instant, Sleep};
+use tokio::time::{sleep, Sleep};
 
 use core::future::Future;
 use core::pin::Pin;
@@ -16,7 +16,7 @@ pin_project! {
         #[pin]
         stream: Fuse<S>,
         #[pin]
-        deadline: Sleep,
+        deadline: Option<Sleep>,
         duration: Duration,
         items: Vec<S::Item>,
         cap: usize, // https://github.com/rust-lang/futures-rs/issues/1475
@@ -27,7 +27,7 @@ impl<S: Stream> ChunksTimeout<S> {
     pub(super) fn new(stream: S, max_size: usize, duration: Duration) -> Self {
         ChunksTimeout {
             stream: Fuse::new(stream),
-            deadline: sleep(duration),
+            deadline: None,
             duration,
             items: Vec::with_capacity(max_size),
             cap: max_size,
@@ -45,7 +45,7 @@ impl<S: Stream> Stream for ChunksTimeout<S> {
                 Poll::Pending => break,
                 Poll::Ready(Some(item)) => {
                     if me.items.is_empty() {
-                        me.deadline.as_mut().reset(Instant::now() + *me.duration);
+                        me.deadline.set(Some(sleep(*me.duration)));
                         me.items.reserve_exact(*me.cap);
                     }
                     me.items.push(item);
@@ -67,7 +67,9 @@ impl<S: Stream> Stream for ChunksTimeout<S> {
         }
 
         if !me.items.is_empty() {
-            ready!(me.deadline.poll(cx));
+            if let Some(deadline) = me.deadline.as_pin_mut() {
+                ready!(deadline.poll(cx));
+            }
             return Poll::Ready(Some(std::mem::take(me.items)));
         }