If you are like me who uses Gmail for emails but not for chatting, there’s a simple setting that will help you completely remove (and not just hide) the chat box from your Gmail mailbox.
Go to your Gmail Settings page, switch to the Chat tab, choose “Chat Off” and click the “Save Changes” button. Alternatively, you may use this link to directly access your Gmail Chat settings page. You can re-enable chat in your Gmail by using the “Chat On” option.
This setting to disable chat may have been available in regular Gmail accounts for some time (am not too sure) but it was only recently added to Gmail for Google Apps accounts.