Instructions
Press the "X" button on your controller if you are involved in a private chat and want to get out. This usually removes the speech bubble from your name, for a brief period of time.
Press the silver Xbox Guide button on your controller, if you're still seeing chat bubbles next to your name. You can disable Voice Chat completely by accessing the Xbox Guide.
Go to Account Management, and select your Xbox Live account.
Select the "Account Settings."
Select the "Voice" option, and disable it.