First of all- don't panic!! The best thing you can do is collect the eggs as often, as possible. No eggs sitting around, no eggs to eat... I have had issues with egg eaters for awhile, and then it stops happening. If the behavior does not stop-try to catch the offender and get rid of her. No need to get rid of other birds. Good luck!
When I was a kid we had a hen that kept eating her eggs and well, any egg that was not picked up or was left unattended for any length of time. We eventually had to have an early morning watch to find the culprit.
I would say try and find out who your 'egg eater' is and either sell, give away, or (if you do this) butcher the chicken. If you sell her with the knowledge that she is an egg eater, she would probably become a meat chicken any way because I know of no way to break a chicken from egg eating but don't get rid of all your chickens, just the one doing the bad deed.
I've heard that if you blow out an egg, then fill the shell with mustard and let the hen eat it, it will break her of the habit. Not sure if it works, but it would be worth trying so you don't have to butcher! Good luck.
Please tell me how you did this and if I ever have the problem with mine I will try it because I was never told any ideas about how to break them from this.....the idea of getting rid of one of my birds makes me want to cry
First, make sure she isn't eating them because she doesn't have food and is hungry. That can make it worse.
I put golf balls and plastic easter eggs all around in the run and in nestboxes when I have an egg-eating hen. They will peck them apart but find nothing inside. Once or twice I almost tried the filling an egg with mustard, hot pepper or mud. But they stopped before that.
Also, try darkening the nest boxes and raising them if they aren't already a foot and a half or two feet high.
If you have a second pen or coop try moving her to it if nothing else works, I've had birds I've moved and they have stopped, then when moved back they didn't start the bad habit again.
Hot pepper won't work as they have no receptors for hot, but I've read occasionally of mustard working. I've read more often, I think, of scattering lots of golf balls / other fake eggs around. Fortunately I never had to deal with this.
Others can learn the habit from the egg eater, so if you can identify and isolate, that would be good.
Now that you say it, I remember that too, they cannot feel the hot from peppers. That would explain why they don't mind hot peppers.
Another thing to prevent broken eggs when laid is to make sure the bottom of the nest box has some nesting material on it if it is hard. I use some plastic buckets, and they typically kick all the bedding out, but the egg generally lands on the side and rolls to the bottom, and doesn't crack.
Also, it is good to make sure they have adequate nesting boxes (1 per 3-4 hens) and they are all about the same height, darkness, etc., so they don't favor one and all lay in that one. That way when a hen walks in to lay, less of a chance she will accidentally break any.