egg eating chicken
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It sounds like stress and/or boredom to me. If she is out in the yard, she can scratch and run about and hunt for bugs etc. If she is confined with nothing else to do and she knows that egg tastes good, you can't blame her for eating it.
Usually it starts when an egg gets accidentally broken, maybe as a result of it being thin shelled. Once they know it tastes good and they are locked up with it, it's just too much of a temptation.
She's not stupid, she is just telling you that the answer is to let her out in the yard more or give her a bigger run (cage) or if that is not possible, make the run more interesting with things she can jump up on and scratch through... Hang greens up for her to peck at, scatter clean straw down..... mine can't resist a pile of new straw even though they free range. Dig up some dirt from the garden or compost and throw it in so that there are bugs for her to scratch for.... make her life more interesting basically.
What are you feeding her and how many chickens do you have? Is she the only one illustrating egg eating behavior?
You need to stop this behavior asap or it will never stop. Get the aggs out of the nest immediately add some golf balls or other egg replacemts that wont break when she pecks at them and try boosting her diet by adding more protien.