I have chat turned off, but it still shows that I'm online (with a green dot indicator). I don't want everyone to know when I'm online in Facebook. How can I eliminate the green light from showing when I'm signed on to my Facebook? This is a privacy concern.
IF you have an app which manages chat for you, such as Pidgin or Trillian, it could override the browser's web chat if you are logged into chat with them. Otherwise, if you disable chat in facebook, you should not be visible as online. If you are, it is a bug, and your only option at that point is to report it to Facebook.