if you do not want your presence known by friends, this is the right solution for your reply
Here are step by step How Invisible on Facebook Chat
1. Login to your facebook account
2. go directly to the link application Appear Offline
3. Alow Appear Offline application and you will be able to see who your friends are online, although the status of your facebook chat offline (invisible): D
4. Facebook allows you to access the application Appear Offline, click the Bookmarks menu on its application Appear Offline;).
hopefully useful !!