You're in the US, right? In that case, if you were told this would be a "condition of employment" before you were hired
then, yes, it probably is legal and probably can be enforced. Checking with a lawyer is always a good idea in order to understand the dynamics of the situation, and maybe to learn some other options.
If you simply want to ensure privacy with regard to internet use and email, it might be easiest to pick up an inexpensive used computer, and that would probably be cheaper than a consultation with a lawyer.
EDIT: By the way, please don't consider any of this as an indication that I believe your employer is being either reasonable or rational -- just that it's probably legal. I was in a similar position once, many years ago. Seriously, good luck.
Edited by Capn Easy, 06 July 2011 - 08:33 PM.