Sex drives the evolutionary process.
It is through sex that varying genomes can be combined and a different result than the two parents appears. Now does this child have different properties than its parents (within genetic reason)? Yes, its eyes may be a different color, its brain is certainly different, as are its immune system, etc. Now if you take this line of reasoning and expand the sexual lineage down thousands of generations you will see that the great great great, etc. grandchild of this couple will have extremely different properties than the original parents. And if you go far enough (millions of years), odds are the far distant offspring may not even be able to mate with its original ancestors)
Thus evolution of a species through sexual reproduction.
Hence, answering the question that the egg came before the chicken, or at least the chicken as we know it today.