Our team mostly have the sidebar collapsed to the side, and thus do not see the red 'pip' on chats with unread messages. The Chat module being an area one has to navigate to or slide open, not always open and visible, it somewhat defeats the purpose of unread notifications only shown on the chats after one looks there, i.e there is no prompt to check Chat messages.
It would be helpful, and consistent with the existing 'Inbox' notifications behaviour, to have a numerated pip on the Chat icon on the sidebar.