A new chat request is a message that has been initiated by another member to yourself.
Click on "Chats" in the top bar and you will be taken to your "Chats" home page.
This "Chats" home page shows all your open, closed and new chat requests received..
The below diagram illustrates how to accept or decline a new chat request.
Any new such chats are found under the tab "New Chat Requests."
Simply click the tick to accept or the x to decline.