How to Block Annoying People on Facebook Chat
Is someone annoying pestering you on Facebook chat? Just move them on your "Blocked list."
Steps
1 Click 'Chat' (bottom right hand corner), then select the Preferences icon.

2 Select 'Turn Off Chat...' from the drop-down menu.

3 Select 'Turn off chat for only some friends...'

4 Drag a group name or the individual names of friends to the new list box.

5 Click 'OK.' These people will not be able to chat with you, but you will be able to see wall posts and messages.
(Source: WikiHow)