This are actually not my words, i quote this from SumGuy3, but i strongly agree with him on this.
"There should be an option to turn on notifications for group chat rooms. Something similar to when a friend messages you, but maybe just have the tab flash and no sound (or make them both toggle-able options).
I recently tried the group chat with my friends and I found it pretty annoying that there was no way to know if somebody said anything unless you are watching the chat. This probably isn't a big deal in large groups, but it seems like one of those small things that could make the game more friendly with people who have just a small group of friend that they play with often.
If this option already exists, please let me know."