diff --git a/libavformat/internal.h b/libavformat/internal.h
index 49e82bfbca..f45b1cd6b4 100644
--- a/libavformat/internal.h
+++ b/libavformat/internal.h
@@ -142,6 +142,11 @@ struct AVFormatInternal {
      * Prefer the codec framerate for avg_frame_rate computation.
      */
     int prefer_codec_framerate;
+
+    /**
+     * Set if chapter ids are strictly monotonic.
+     */
+    int chapter_ids_monotonic;
 };
 
 struct AVStreamInternal {
diff --git a/libavformat/utils.c b/libavformat/utils.c
index 1ec71691e5..9dab4fc96f 100644
--- a/libavformat/utils.c
+++ b/libavformat/utils.c
@@ -4614,9 +4614,14 @@ AVChapter *avpriv_new_chapter(AVFormatContext *s, int id, AVRational time_base,
         return NULL;
     }
 
-    for (i = 0; i < s->nb_chapters; i++)
-        if (s->chapters[i]->id == id)
-            chapter = s->chapters[i];
+    if (!s->nb_chapters) {
+        s->internal->chapter_ids_monotonic = 1;
+    } else if (!s->internal->chapter_ids_monotonic || s->chapters[s->nb_chapters-1]->id >= id) {
+        s->internal->chapter_ids_monotonic = 0;
+        for (i = 0; i < s->nb_chapters; i++)
+            if (s->chapters[i]->id == id)
+                chapter = s->chapters[i];
+    }
 
     if (!chapter) {
         chapter = av_mallocz(sizeof(AVChapter));