How do I go offline in Facebook Chat?
You can go offline (unavailable) to all friends, some friends or individuals:
To go offline to all friends: Click the icon at the bottom of the chat sidebar and select Go Offline.
To go offline to specific friends or friend lists: Click the icon at the bottom of the chat sidebar and select Advanced Settings. Enter the names of friends or friend lists you want to appear offline to next to the heading All your friends see you except.
Note: If you are online to chat but appear offline to friends, make sure that those friends aren’t included in a friend list under: All your friends see you except.
via How do I go offline in Facebook Chat? – Facebook Help Center.
Gregory Reese Research 