The eggy smell is sulfur, which can be released by some types of bacteria. If your chicken smells eggy and it came out of a cling-wrapped or regular plastic package, it’s probably best not to eat it. On the other hand, sometimes an egg smell can be a result of the cryovac packaging process. If your chicken was cryovac packaged, let it sit for a few minutes to see if the smell dissipates. If it does, it is likely safe to eat if you cook it thoroughly.