The question is whether or not the egg being refered to is a chicken egg. And then it further depends on whether someones interpretation of a chicken egg is an egg that has a chicken in it, or an egg laid by a chicken. If its an egg that has a chicken in it, then yes the egg came first but if its an egg laid by a chicken, then the chicken came first as the thing that laid the egg that housed the chicken was itself not a chicken and therefor its egg was not a chicken egg.