Instructions
Close World of Warcraft.
Go to the WoW Interface website's "HideChatButton" page.
Download the HideChatButton add-on by clicking "Download" at the top of the page.
Unzip the file in the "Interface" > "Add-ons" folder for your World of Warcraft game.
Open World of Warcraft. Navigate to the "Character Select" screen, and enable the HideChatButton add-on.