chicken and egg, what's the problem?

We got here either by evolution or creation.

Evolution

Chickens evolved from other birds, which of course laid eggs.
The first bird that could definitely be called a chicken hatched from an egg laid by a bird that was not quite a chicken
The egg came first

Creation:

God created the world with fully formed animals, not eggs.
The chicken came first

Intelligent design, if you're woolly minded enough to believe in that:

God assembled the chicken genome, and ensured the development of the resultant embryo, which would then have developed in an egg, laid by another earlier kind of bird.
The egg came first.