My friends and I love the game, but love the public/private chat a lot too. However, when new messages are posted the only way to know is to check on the game manually. We'd really like to see a 'new chat' notification feature added.
In the new Unity client, the number of unread chat messages appears next to chat. Be sure to check it out!
Agreed, this would be nice. Wish I had more votes to give.