I'm not raising my own chickens yet, but I've read a bunch of places that you shouldn't let the chickens eat egg or egg shells because they will then associate their eggs with food and eat them before you get a chance, or before they can brood on them to hatch. Is that really a concern? Have you seen any problems with it in your coop?
I personally have never seen this as a problem with my hens.
I think part of it is in the presentation. We give our girls hard boiled or scrambled eggs on occasion, especially in the winter, when their free ranging source of protein is low, and the cold causes them to burn more energy to keep warm. When I prepare the eggs, I make sure the scrambled eggs are well broken up, and the hard boiled eggs get smushed and then chopped up with the shell on into smaller bits. I never present them with a whole cooked egg. Eggshells get added to their regular food dish, and are crushed up small enough to be bit sized.
Remember, chickens are as trainable as your dog - probably moreso. If you choose a specific dish to provide them treat foods like eggs, cooked oatmeal, thawed frozen vegetables, etc., in, they will recognize that dish and know it to contain food. If you also give them this treat at the same time of day every time, that will help them have an expectation. I use an old, large, shallow clear glass pie plate. When my girls see that pie plate, they get all excited. As soon as I set it down, they are all over it, gulping down food faster than the dogs do for meat scraps!
As part of training your chickens, select specific times of day to get the eggs. Collect them several times a day - you will learn what times of day your chickens lay; it does appear to vary with the seasons. In the winter, you want to be collecting several times a day just to avoid frozen eggs. The chickens seem to learn that the eggs are yours and not theirs.
But have consideration for your chickens as well. I know with mine, and their propensity for all using the same nesting box, it's often very like the women's restroom at a concert - a line waiting for the box, and as one pops out, another pops in. I do try to show them respect and not reach under the hen in the box for the other eggs; however, if she she's in there for more than half an hour, I will reach in and get the eggs to keep the hen in question from getting broody. I've been complained at - that usually means she still needs to lay - and been pecked only once. But I make sure they know the eggs are mine. I do thank them though - never underestimate what animals understand.
The only times I've seen my hens eat uncooked eggs was two occasions - the first is when I accidentally drop one when collecting eggs, and it breaks. At that point, it's a loss to me, but there is nutrients to be had for the chickens.
The other time was in their early egg laying days, when the occasional egg would be laid without a shell. Those eggs are still edible by us; they just lack the protective shell and instead have a thick membrane. Usually, the one who started eating the egg was the hen who laid it. I believe this is an instinctual thing; the hens know that this egg could never possibly be fertile, and so is a waste. It is very akin to mammals eating the afterbirth; an extra source of nutrients. These eggs are rare, and mainly happen when the chickens first start laying and their bodies are getting used to the whole process of creating that egg. However, if you find it in older chickens, it is a sign that they are lacking calcium and it is something you need to remedy as soon as possible.
This all being said, and while I've never seen it in my girls, some hens and roosters can become cannibalistic in regards to the eggs (as well as other chickens, but that is a topic for another time), breaking all the eggs that are laid, and eating some as well. This bodes ill if you are planning to raise chicks of your own and allow the hens to hatch their own eggs - the chicken in question becomes a killer. While you can trim their beaks, this could lead to health issues for that chicken, especially if you allow them to forage. The best course of action is to cull that chicken. Sounds uncivil, but remember, chickens are working animals, no matter how you name them, or treat them as pets. The job of my girls is, right now, to produce eggs. If one of them is destroying the eggs, she has become a detriment to the flock - and us - and would better serve us in the roaster or the stock pot.
Thanks for the question, hope this answer helps, and feel free to ask more at any time!