If you are able to type in chat, but it disappears when you press Enter, it means they have disabled game chat.
Also, just to double check, go into your own live chess settings page
http://www.chess.com/home/livechess_settings.html
6th box UP from the bottom of the page. Make sure the box marked
'Never Chat" is not checked. (If it is, then UN-check that box, save settings, then go into live chess and it'll work then)
If your chat is enabled, and you did not click on the 'disable game chat' text within the game chat window, then you can safely assume your opponent disabled it
I've been trying to chat with my opponent during the game, but can't respond. I have followed the directions as stated (click into the box and hit enter under "Game") but still nothing. What am I missing?