Quote Originally Posted by krazyrs View Post
PC: right click > hide chat window
PS4: L1 + Pad Button
L1 + Pad hides or displays the entire HUD. PS4 pad (or PS3 Select) to select the chat window, followed by square button (right-click equivalent), will bring up the "hide chat window" option.

I don't know of a macro or text command for it, though.