If you want to concentrate on play without being distracted by conversation, or maybe its just one specific game you don't want to chat in, either way we've got you covered!
Disabling Chat in a Single Game
In the upper right of the chat window there is a small icon that looks like a chat bubble with an 'x' in it. Clicking this icon will ensure that there is no more chat allowed in the game, and will remove any of the previous chat from the screen. Note that this action is irreversible, and chat will be disabled for the rest of the game.
Disabling Chat for All Games
If you want to disable chat for ALL of your games, you can go into your Live Chess and Daily Chess settings and set the 'Game Chat' option to 'friends only' or 'nobody'. This will limit who can chat with you in your games.
Be sure to click 'save' to put the new setting into effect! And remember there is a separate setting for Live chess and Daily chess!