In theory there must have been a point along the evolutionary chain where something that was not quite a chicken laid an egg containing an embryo with enough gentic difference to make it a chicken therefore making it a chicken egg.
If you define a chicken egg as that which is laid by a chicken rather than that which contains a chicken then the chicken came first.
JOKE...
A chicken and egg lie on a messed up bed, panting slightly.
"Well, that answers that question" says the chicken.