Did the hen only eat one egg or has this been a habit? Are the eggs she is eating good, hard shelled eggs, or were they soft shelled/no shell that she's eating?
I remember when I first got chickens, I was startled at one that would peck hard shelled eggs open and start chowing down. Once in a while they still do it - a few times they were those soft shelled eggs that weren't good at all so she pecked them. From time to time we still have one peck a hole in another egg and leave it like that. It's something that happens so just gotta roll with it at times.
The best thing we did is go to collect eggs twice a day (once in the later morning and once in the evening) - this will be easier when you know about what times your chickens lay. After a while, we didn't need to do twice a day anymore, only once a day. This gives the chicken less opportunity to eat it.
Make sure they are getting enough calcium from oyster shell/crushed eggshells (be sure eggshells are pulverized so they don't associate them with their own eggs) in their food or in a separate bowl. Be sure they are getting a good layer feed. Make sure there are adequate nesting boxes (I think sometimes chickens want to use a nesting box, see another egg in it and aren't happy about that). Make sure the nesting boxes are as dark as possible to avoid stress. I've heard as a last resort, some people poking holes on both ends of the eggs, blowing out the contents into a bowl and then filling it with yellow mustard and putting it in the nesting box so they associate it with a bad taste (never tried this).
Some say try a wooden egg or a golf ball so they will get turned off to pecking.
My chickens eat the eggs that get broken in the nesting box because the shells are a soft despite having plenty of oyster shell, free ranging all day and also eating shells from the eggs I cook.
This began with the third flock I purchased from a different source than the first two flocks. I have tried wooden eggs but it doesn't help. Just makes more of a mess. Key for me is to collect asap. Even then, some of the eggs have hairline cracks.
What I am saying is, try to notice if the egg shells are just too soft & you might consider not getting the birds from the same place again.
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