It's a good idea to turn off Facebook chat to avoid being messaged by friends and family when you log into your Facebook account. Unless you turned off Facebook's chat program at the end of your previous Facebook session, the program automatically logs you in when you log into Facebook the next time. It only takes a few seconds to change the Facebook status and appear offline.
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Navigate to the Facebook website.
Enter the email and password associated with your Facebook account. Your Facebook profile opens up.
Click the "Chat" box in the lower-right corner of the screen. The Chat box expands upward.
Click "Options" in the upper-right corner of the Chat box and then click "Go offline." The online status for your Facebook account is now turned off.