Can a Chicken live by eating only its own eggs?

One hen could not live on the one egg she might produce per day, because laying an egg takes a lot of resources from the hen's body, and in addition to these she would need extra to maintain her own body apart from the demands of laying her egg. Also, not all the egg is edible - she wouldn't be able to reclaim the calcium required to make the next shell.

What would happen if you tried this is that she would rapidly stop laying, in order to reduce the demands on her system and to survive. Consequently, no egg to eat the next day!

If your question means, could a hen live on eggs alone if she had enough eggs provided for her by other hens, I suppose she could, for a while, but it would probably upset her gut because she wouldn't have enough roughage in her diet to grind up food in her gizzard. Also, of course, the nutrients would be right out of balance, with far too much protein in an egg designed to feed a growing chick, and too little carbohydrate to keep a hen warm and active, part from other digestive problems. If a hen is poorly and not eating well, or is moulting, cooked egg can be a valuable protein supplement in the short term, but it's not suitable as a main diet.

NO a chicken needs "grit" in their diet to help them break their food down for digestion. Chickens know when they need grit (tiny pebbles and rocks<grit)

I would think they could if had enough but would not be healthy for them since it can't supply all the growing needs they need.

I think they could but a friend on mine fed her chickens chicken and they "loved it" she said

O.o