When you view a game on your droid, press the Menu button. You should then see the 'Chat' bubble.
Which droid model and version are you using?
When the latest app update was released, did you install it over the one on your device ? or did you close the app, completely un-install, then install the new app ?
Can you go into settings /manage applications / chess.com
clear data and force stop, then un-install and go back onto the market place and re-install the app.
I AM PAYING A HUNDRED DOLLARS A YEAR FOR THIS SITE AND EXPECT A FEW BASIC FEATURES TO WORK LIKE CHAT WHERE IS THE CHAT BUTTON PLEASE RESTORE THIS I CANT FIND IT ANYWHERE THIS IS DUMB AND MY DROID APP HAS BEEN DOWN ALL FAY AND NO REPLY FOR YOU TO FIX IT I NEED HELP AND NEED IT NOW!