Appear Offline to Certain Users on Facebook Chat
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.
When you pop open the chat window, you can find all your friends who are currently signed into chat. If you have created any friend list, they will appear under that list. All your lists can be viewed by clicking on Friend Lists at the top.