First, make sure it isn't a crow. I have crows nearby and they sometimes go into the coop, help themselves to an egg and fly away with it. But I noticed crow pecking at a duck egg which had just been laid outside.
If she really is an egg eater, good luck! I adopted Hannibelle the Cannibelle thinking I could change her behaviour. She never laid an egg but ate any she could get her beak on. Cayenne pepper? Yum! She liked a bit of spice. So every morning she would be sent out into the main yard until most of the other chickens had finished laying their eggs and I had collected them.
This got really tiresome after a year or so. I rehomed her to a farm that adopts unwanted chickens. The owner keeps her in a run with pullets who haven't started laying yet.