Is it safe to feed eggs to cats?

My kitty needs to take off some weight, but begs constantly. After some research, I think upping the amount of protein in his diet would help (kind of like Atkins), however, I really can't afford a more expensive brand of cat food. So, I thought if I mixed boiled eggs (or egg whites) into his food, he'd feel fuller, get more protein, and not be taking in a lot of extra calories. Plus, eggs are cheap. Has anybody done this? Will eggs harm cats?