Update -
If you want to disable your chat, type this into your console;
hud_saytext_time 0
To re-enable chat, type this into your console;
hud_saytext_time 12
This command essentially changes how long chat messages appear in the corner. When you set it to 0 they show for zero seconds which is essentially just hiding chat at that point. The default is 12 but if you want chat messages to show for longer, or less time change the 12 to something else.