I don't get why people think this is such a hard question. One solution is that God or Allah or Jehova or whoever made the chicken. Another is of course that the egg came first as a result of mutation, evolution, or similar from another species. Probably a bird that decided to mate with a little dinosaur or something... Sick bastards...
So when it comes down to it, it's a matter of faith. Either some god (or THE God) or scientific evolution