Hiding the chat button is nice by hiding the left app bar, but it's a bit annoying to have to toggle it on and off. Not sure if there would be an option to have the chat shortcut be in the main menu to the right of the compose button, so all you have to do is hover over the main menu and click the chat button from there?
Keep the left app bar toggle just adding an option to have another quicker way to get to your chats.