diff --git a/yt_dlp/downloader/youtube_live_chat.py b/yt_dlp/downloader/youtube_live_chat.py
index 8e173d8b58..a6c13335e5 100644
--- a/yt_dlp/downloader/youtube_live_chat.py
+++ b/yt_dlp/downloader/youtube_live_chat.py
@@ -79,8 +79,7 @@ def download_and_parse_fragment(url, frag_index, request_data):
 
         self._prepare_and_start_frag_download(ctx)
 
-        success, raw_fragment = dl_fragment(
-            'https://www.youtube.com/watch?v={}'.format(video_id))
+        success, raw_fragment = dl_fragment(info_dict['url'])
         if not success:
             return False
         try:
diff --git a/yt_dlp/extractor/youtube.py b/yt_dlp/extractor/youtube.py
index 6c93517d44..57300114d4 100644
--- a/yt_dlp/extractor/youtube.py
+++ b/yt_dlp/extractor/youtube.py
@@ -2150,6 +2150,7 @@ def process_language(container, base_url, lang_code, query):
                 # This will error if there is no livechat
                 initial_data['contents']['twoColumnWatchNextResults']['conversationBar']['liveChatRenderer']['continuations'][0]['reloadContinuationData']['continuation']
                 info['subtitles']['live_chat'] = [{
+                    'url': 'https://www.youtube.com/watch?v=%s' % video_id, # url is needed to set cookies
                     'video_id': video_id,
                     'ext': 'json',
                     'protocol': 'youtube_live_chat_replay',