If you go to the person's contact panel, you will see "block user".
See if that works.
If not, then simply let me know who the person is, they will lose their account with a swiftness.
No time for that.
Now, if they don't have an account, you can set your page to private like the others mentioned. Only your friends can see your page.
It amazes me, I'm dealing with a stupid moron at work, there is ALWAYS someone lurking around trying to cause problems.
Good luck.