While not exactly what you asked for, a couple new features should help with that sort of problem. You can hide the chat box, or delete past messages from it.

From the Patch 2.4 Notes:

The ability to temporarily hide the log window has been added.
Select Hide Log Window from the subcommand menu of the channels bar to temporarily hide the log window. To redisplay the log window, press the Enter key, or when using a gamepad, the BACK, SELECT, or Touch Pad buttons.

The following text commands have been added:
/clearlog, /cl →Delete all past messages from your entire chat log.