The chat was possibly one of the greatest additions to the game, but it could be better. I think having chats marked by numbers separates people, makes it harder to find an active room. So why not just make a few rooms with their own topics? General, help, social, strategy, etc.
Private messaging is something that could be done through both mails and another chat tab. You could message anyone, but also block anyone. A report option for this and the chat would be good to stop the few spammers or those who actively harass others.
Now that people have profiles, making a friend list could work pretty well. It and the previously mentioned messaging would also compliment eachother.