A drawback to the Facebook Chat feature is that your friends can see when you're logged in to the social network. Your friends can, at any time, interrupt you while browsing by sending you a Chat message. However, Facebook has incorporated several Chat filters so you can block your online status from your friends if you wish. You can block a selection of friends or all of your friends at once.
Click the "Chat" box at the bottom of the window to open the sidebar, if it isn't already open. The sidebar displays a list of recent activity and a list of friends who are currently online.
Click the gear wheel icon at the bottom of the sidebar and select "Advanced Settings" to view the Advanced Chat Settings window.
Click the radio button next to "Turn on chat for all friends except" and then enter the names of the people you want to block from seeing when you're online. If you want to appear online to only a few of your friends, click "Turn on chat for only some friends" and enter the names of the people that you want to see when you're online. If you want to block everyone, click "Turn off chat."
Click "Save" to confirm the setting.
Another option to block everyone from seeing your online status is to click the gear wheel icon and select "Turn Off Chat."