DON'T EAT THE EGG!
Strange though, eggs were what I craved in my first couple of weeks.
Just think of it as psychological... Your body DOES NOT need that egg, as you are giving it all the vitamins and nutrients it needs, and you're getting energy from burning fat. I'm afraid the craving is all in your head...
And I agree, its not the egg that is the big problem (although it won't help your weightloss), but if you have and egg now, then you'll start thinking its ok to have something tomorrow, and the day after, and then before you know you'll be picking everyday..
Try and be strong and stay 100% my love, you'll be thankful for doing so at your weigh in!
Good luck!