By default, the Chat bar and any active chat sessions are always open on the site. If you want to hide the Chat bar, just select the arrow icon to the right of the Chat tab.

If you want to disable the Chat function completely, head to My Profile, then select Settings from the drop-down list. Select the Privacy tab on the left, then check the box next to Disable Chat, which will hide the Chat site wide.

If you want to go offline from the Chat but not disable it, all you need to do is select Go Offline from the menu. See image below.