diff --git a/lib/media/media_source_engine.js b/lib/media/media_source_engine.js
index 21d2a94cab8..72fd2e8262f 100644
--- a/lib/media/media_source_engine.js
+++ b/lib/media/media_source_engine.js
@@ -696,11 +696,28 @@ shaka.media.MediaSourceEngine = class {
               goog.asserts.assert(
                   box.version == 0 || box.version == 1,
                   'TFDT version can only be 0 or 1');
-
-              const parsedTFDTBox = shaka.util.Mp4BoxParsers.parseTFDT(
-                  box.reader, box.version);
-              const baseTime = parsedTFDTBox.baseMediaDecodeTime;
-              startTime = baseTime / timescale;
+              const Mp4BoxParsers = shaka.util.Mp4BoxParsers;
+              try {
+                const parsedTFDTBox = Mp4BoxParsers.parseTFDT(
+                    box.reader, box.version);
+                const baseTime = parsedTFDTBox.baseMediaDecodeTime;
+                startTime = baseTime / timescale;
+              } catch (error) {
+                if (error.code != shaka.util.Error.Code.JS_INTEGER_OVERFLOW) {
+                  throw error;
+                }
+                if (!window.BigInt) {
+                  throw error;
+                }
+                const parsedTFDTBox = Mp4BoxParsers.parseTFDTAsBigInt(
+                    box.reader);
+                const baseTime = parsedTFDTBox.baseMediaDecodeTime;
+                const startTimeBigInt = baseTime / BigInt(timescale);
+                if (startTimeBigInt > Number.MAX_SAFE_INTEGER) {
+                  throw error;
+                }
+                startTime = Number(startTimeBigInt);
+              }
               parsedMedia = true;
               box.parser.stop();
             }).parse(data, /* partialOkay= */ true);
diff --git a/lib/util/data_view_reader.js b/lib/util/data_view_reader.js
index fb7db36b316..9079476db59 100644
--- a/lib/util/data_view_reader.js
+++ b/lib/util/data_view_reader.js
@@ -174,6 +174,42 @@ shaka.util.DataViewReader = class {
   }
 
 
+  /**
+   * Reads an unsigned 64 bit integer, and advances the reader.
+   * @return {bigint} The integer.
+   * @export
+   */
+  readUint64AdBigInt() {
+    /** @type {number} */
+    let low;
+    /** @type {number} */
+    let high;
+
+    try {
+      if (this.littleEndian_) {
+        low = this.dataView_.getUint32(this.position_, true);
+        high = this.dataView_.getUint32(this.position_ + 4, true);
+      } else {
+        high = this.dataView_.getUint32(this.position_, false);
+        low = this.dataView_.getUint32(this.position_ + 4, false);
+      }
+    } catch (exception) {
+      throw this.outOfBounds_();
+    }
+
+    if (!window.BigInt) {
+      throw new shaka.util.Error(
+          shaka.util.Error.Severity.CRITICAL,
+          shaka.util.Error.Category.MEDIA,
+          shaka.util.Error.Code.JS_INTEGER_OVERFLOW);
+    }
+
+    this.position_ += 8;
+
+    return BigInt((high * Math.pow(2, 32)) + low);
+  }
+
+
   /**
    * Reads the specified number of raw bytes.
    * @param {number} bytes The number of bytes to read.
diff --git a/lib/util/mp4_box_parsers.js b/lib/util/mp4_box_parsers.js
index 49b2d2e318c..b065ffd2137 100644
--- a/lib/util/mp4_box_parsers.js
+++ b/lib/util/mp4_box_parsers.js
@@ -66,6 +66,17 @@ shaka.util.Mp4BoxParsers = class {
     };
   }
 
+  /**
+   * Parses a TFDT Box.
+   * @param {!shaka.util.DataViewReader} reader
+   * @return {!shaka.util.ParsedTFDTBoxAsBigInt}
+   */
+  static parseTFDTAsBigInt(reader) {
+    return {
+      baseMediaDecodeTime: reader.readUint64AdBigInt(),
+    };
+  }
+
   /**
    * Parses a MDHD Box.
    * @param {!shaka.util.DataViewReader} reader
@@ -291,6 +302,20 @@ shaka.util.ParsedTFHDBox;
  */
 shaka.util.ParsedTFDTBox;
 
+
+/**
+ * @typedef {{
+ *    baseMediaDecodeTime: bigint
+ * }}
+ *
+ * @property {bigint} baseMediaDecodeTime
+ *   As per the spec: the absolute decode time, measured on the media
+ *   timeline, of the first sample in decode order in the track fragment
+ *
+ * @exportDoc
+ */
+shaka.util.ParsedTFDTBoxAsBigInt;
+
 /**
  * @typedef {{
  *    timescale: number,