Chickens love to peck. Normally though they do not peck their own eggs but when it starts and nothing is done to keep them from doing it, they would develop the taste of the eggs and the habit could form. To prevent chickens from eating their eggs, try the following.
Feed your chicken grits. Grits are purchased in your local farm supply store or you could make your own. To make grits, roast eggshells until they are brownish and crunchy. Pound the shells and mix it with chicken feed. Chicken that does not have enough calcium in their diet will try to find it elsewhere and eggshells are an alternative source. Make sure that the feed has enough calcium and protein.
When an eggshell is weak, it could easily break and when it does, the chicken will start pecking on it. Weak eggshells are signs that the chicken lacks Vitamin D3, protein, calcium, or has an infection. Check for infection aside from feed composition.
When there are no infections and the feed is sufficient, it could be that the nest box is too hard. Provide padding for the nest to prevent accidents to the egg even when the chicken shuffles and scratches around the nest box. Keep the nest box dark. Chickens are less likely to keep on moving around in darker places. Dark nest boxes keep the chicken relaxed. When hens are less agitated they are less likely to trample on eggs. Limit also the number of chickens in a nest box. A typical nest box could accommodate four hens. Less hen for every nest box is better.
Do not feed the eggshells to the chickens. Gather the shells and clean up the coop, likewise, do not feed the dirtied eggs to chickens. Introducing the chicken to the egg will start them developing a taste for it that could start the habit. Chicken could also start pecking at the eggs if they are bored. Keep them busy by hanging vegetable scraps tied to a string for them to peck.
Collect eggs as often as twice a day if you can. That way you could monitor the production of the eggs better. When the eggs are reduced, and the causes are eggs that were pecked on, isolate the chicken pecking on the eggs. You could find that out when a chicken has egg residues in the beak. When the chicken is isolated, feed the chicken with liquid milk for a while. If isolating the chicken is not possible, try trimming the upper beak.
Another method to prevent the chicken from eating their eggs is to place golf balls in the nest box. Pecking on a golf ball will discourage the habit from forming. If you have done this and the egg supply does not return to normal, find out if rodents are getting into your nest box. Whatever the case though, prevent the chicken from tasting their eggs because when the habit is formed, it will almost be impossible to break.