diff --git a/library/hls/build.gradle b/library/hls/build.gradle
index 4deef3b5f9..152fd35dff 100644
--- a/library/hls/build.gradle
+++ b/library/hls/build.gradle
@@ -33,6 +33,8 @@ android {
         }
     }
 
+    sourceSets.test.assets.srcDir '../../testdata/src/test/assets/'
+
     testOptions.unitTests.includeAndroidResources = true
 }
 
@@ -44,6 +46,7 @@ dependencies {
     compileOnly 'org.jetbrains.kotlin:kotlin-annotations-jvm:' + kotlinAnnotationsVersion
     implementation project(modulePrefix + 'library-core')
     testImplementation project(modulePrefix + 'testutils')
+    testImplementation project(modulePrefix + 'testdata')
     testImplementation 'org.robolectric:robolectric:' + robolectricVersion
 }
 
diff --git a/library/hls/src/test/java/com/google/android/exoplayer2/source/hls/WebvttExtractorTest.java b/library/hls/src/test/java/com/google/android/exoplayer2/source/hls/WebvttExtractorTest.java
index 2f7f8e3fc0..5f1169e222 100644
--- a/library/hls/src/test/java/com/google/android/exoplayer2/source/hls/WebvttExtractorTest.java
+++ b/library/hls/src/test/java/com/google/android/exoplayer2/source/hls/WebvttExtractorTest.java
@@ -17,9 +17,12 @@ package com.google.android.exoplayer2.source.hls;
 
 import static com.google.common.truth.Truth.assertThat;
 
+import androidx.test.core.app.ApplicationProvider;
 import androidx.test.ext.junit.runners.AndroidJUnit4;
 import com.google.android.exoplayer2.extractor.ExtractorInput;
 import com.google.android.exoplayer2.testutil.FakeExtractorInput;
+import com.google.android.exoplayer2.testutil.FakeExtractorOutput;
+import com.google.android.exoplayer2.testutil.TestUtil;
 import com.google.android.exoplayer2.util.TimestampAdjuster;
 import java.io.EOFException;
 import java.io.IOException;
@@ -63,6 +66,27 @@ public class WebvttExtractorTest {
     assertThat(sniffData(data)).isFalse();
   }
 
+  @Test
+  public void read_handlesLargeCueTimestamps() throws Exception {
+    TimestampAdjuster timestampAdjuster = new TimestampAdjuster(/* firstSampleTimestampUs= */ 0);
+    // Prime the TimestampAdjuster with a close-ish timestamp (5s before the first cue).
+    timestampAdjuster.adjustTsTimestamp(384615190);
+    WebvttExtractor extractor = new WebvttExtractor(/* language= */ null, timestampAdjuster);
+    // We can't use ExtractorAsserts because WebvttExtractor doesn't fulfill the whole Extractor
+    // interface (e.g. throws an exception from seek()).
+    FakeExtractorOutput output =
+        TestUtil.extractAllSamplesFromFile(
+            extractor,
+            ApplicationProvider.getApplicationContext(),
+            "webvtt/with_x-timestamp-map_header");
+
+    // The output has a ~5s sampleTime and a large, negative subsampleOffset because the cue
+    // timestamps are ~10 days ahead of the PTS (due to wrapping) so the offset is used to ensure
+    // they're rendered at the right time.
+    output.assertOutput(
+        ApplicationProvider.getApplicationContext(), "webvtt/with_x-timestamp-map_header.dump");
+  }
+
   private static boolean sniffData(byte[] data) throws IOException {
     ExtractorInput input = new FakeExtractorInput.Builder().setData(data).build();
     try {
diff --git a/testdata/src/test/assets/webvtt/with_x-timestamp-map_header b/testdata/src/test/assets/webvtt/with_x-timestamp-map_header
new file mode 100644
index 0000000000..fb4edfdb7b
--- /dev/null
+++ b/testdata/src/test/assets/webvtt/with_x-timestamp-map_header
@@ -0,0 +1,13 @@
+WEBVTT
+X-TIMESTAMP-MAP=LOCAL:1:11:16.443,MPEGTS:384879885
+
+NOTE
+X-TIMESTAMP-MAP is defined in RFC 8216 section 3.5 (HLS spec).
+The cue times below are deliberately greater than 2^33 in 90kHz PTS clock,
+to test wraparound logic.
+
+266:18:35.679 --> 266:18:37.305
+  Cue text one
+
+266:18:37.433 --> 266:18:38.276
+  Cue text two
diff --git a/testdata/src/test/assets/webvtt/with_x-timestamp-map_header.dump b/testdata/src/test/assets/webvtt/with_x-timestamp-map_header.dump
new file mode 100644
index 0000000000..272155e8a8
--- /dev/null
+++ b/testdata/src/test/assets/webvtt/with_x-timestamp-map_header.dump
@@ -0,0 +1,16 @@
+seekMap:
+  isSeekable = false
+  duration = UNSET TIME
+  getPosition(0) = [[timeUs=0, position=0]]
+numberOfTracks = 1
+track 0:
+  total output bytes = 324
+  sample count = 1
+  format 0:
+    sampleMimeType = text/vtt
+    subsampleOffsetUs = -958710678845
+  sample 0:
+    time = 5000155
+    flags = 1
+    data = length 324, hash C0D159A2
+tracksEnded = true