I would add to that -- in the previous setup, we got that red asterisk when we had a new chat message, just like the asterisks for conditional moves, notes, etc. Now you have to specifically open the chat to see if perhaps you have a new message. I'm talking about daily games here on the desktop version. Thanks!
Chat and message notifications

It’s well over a year since the last comment but it’s still an issue. I don’t see a chat comment unless I go into the game. It would be great to have a settings option to choose to have a notification via mobile or email to say a chat message has been left. Or am I missing something??

The android app notifies me when my opponent moves. Why not when he chats? No clue how long I've ignored them without timestamps either. Oof

I had that issue too but I think the problem only exists on the App. I believe we do get such notifications when logged into Chess.Com online.

As I am aware there is a red dot inside game when you have unread chat message, but you have to be inside the game to see it. I would appreciate if there was an option of turning on a red dot (or other mark) visual notifications of unread chat messages on outside game list. Then you see which game to enter to see a chat message.
Dear Chess.com, can you improve the functionality of chat messaging feature within a chess match. The chat feature with the two speech bubbles icon.
Just some of my issues:
1) No date and time stamp of when a chess chat message was sent or received by an opponent.
2) No email notification of a chess chat message sent by an opponent.
3) No indication or icon counter on the dashboard or within a chess match of new/unread chat messages.
Thanks.