Chat during a game is working fine for me.
I'm on an old HP laptop running windows 7 and I'm not having any problems.
You can only send a message when it's your turn to move, and the message is sent along with your move, which you probably already know.
Does your opponent send any messages to you when they move?
Do they have you on their 'ignore' list?
Have you tried to send a private message to anyone? You should be able to do that at any time, even to someone you are not currently playing.
Does any of this help?
<EDIT> I just sent you a private message. See if you can respond to that.