Most chat clients have the option to appear offline while you are still signed in. By appearing offline you can avoid those users with whom you don't want to chat and still continue to chat with those users who you want to.
Unfortunately Facebook Chat doesn't have this feature but you can use Facebook's Friend Lists feature to set who can see you when you’re online.
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Unfortunately Facebook Chat doesn't have this feature but you can use Facebook's Friend Lists feature to set who can see you when you’re online.
Read More Here