It depends upon the literature you read. If you look in the Encyclopaedia Britannica you will find that it is in fact chicken, alphabetically that is.....
The chicken of course! The shell would have developed through evolution as protection for the chick, but without a chicken in the first place there could not be an egg!
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.