diff --git a/stdlib/public/Concurrency/DispatchGlobalExecutor.cpp b/stdlib/public/Concurrency/DispatchGlobalExecutor.cpp
index fee1a5f646dd9..844984a81dbd3 100644
--- a/stdlib/public/Concurrency/DispatchGlobalExecutor.cpp
+++ b/stdlib/public/Concurrency/DispatchGlobalExecutor.cpp
@@ -276,6 +276,13 @@ void swift_task_enqueueGlobalWithDelayImpl(SwiftJobDelay delay,
   job->schedulerPrivate[SwiftJobDispatchQueueIndex] =
       DISPATCH_QUEUE_GLOBAL_EXECUTOR;
 
+  // dispatch_time takes a signed int64_t. SwiftJobDelay is unsigned, so
+  // extremely large values get interpreted as negative numbers, which results
+  // in zero delay. Clamp the value to INT64_MAX. That's about 292 years, so
+  // there should be no noticeable difference.
+  if (delay > (SwiftJobDelay)INT64_MAX)
+    delay = INT64_MAX;
+
   dispatch_time_t when = dispatch_time(DISPATCH_TIME_NOW, delay);
   dispatch_after_f(when, queue, dispatchContext, dispatchFunction);
 }
diff --git a/test/Concurrency/Runtime/async_task_sleep.swift b/test/Concurrency/Runtime/async_task_sleep.swift
index 42b792d5f1b8c..ec242a1132c28 100644
--- a/test/Concurrency/Runtime/async_task_sleep.swift
+++ b/test/Concurrency/Runtime/async_task_sleep.swift
@@ -18,6 +18,7 @@ import Dispatch
   static func main() async {
     await testSleepDuration()
     await testSleepDoesNotBlock()
+    await testSleepHuge()
   }
 
   static func testSleepDuration() async {
@@ -45,4 +46,31 @@ import Dispatch
     // CHECK: Run second
     await task.get()
   }
+
+  static func testSleepHuge() async {
+    // Make sure nanoseconds values about Int64.max don't get interpreted as
+    // negative and fail to sleep.
+    let task1 = detach {
+      try await Task.sleep(nanoseconds: UInt64(Int64.max) + 1)
+    }
+    let task2 = detach {
+      try await Task.sleep(nanoseconds: UInt64.max)
+    }
+
+    try! await Task.sleep(nanoseconds: UInt64(pause))
+
+    task1.cancel()
+    task2.cancel()
+
+    // These should throw due to being canceled. If the sleeps completed then
+    // the cancellation will do nothing and we won't throw, which is a failure.
+    do {
+      _ = try await task1.value
+      fatalError("Sleep 1 completed early.")
+    } catch {}
+    do {
+      _ = try await task2.value
+      fatalError("Sleep 2 completed early.")
+    } catch {}
+  }
 }