If you want to always have it disabled, you can change that in your Live chess settings. The gear icon under the the one to resize the board (also in the main menu at the bottom) will take you to the options; the last tab with the bell icon for alerts. Or at least, I think that will turn off chat by default -- it may be for just chat alerts.
I'd have to start a live game to check but I think there is an icon on the chat window/area of a circle with a line through it that will disable on a per chat basis.
How do you disable chat in the new V3? I don't want idiots trash-talking during the game like they think they're some hot shot even though any half decent player would crush them.