If the question is just "The chicken or the egg" then of course the egg came first because he first chicken ever had to come from an egg.
Now if you change that to "The chicken or the chicken egg" it get's a bit more difficult. The first chicken ever was hatched from an egg, but do you call that a chicken egg? It did contain a chicken but the chicken that was in that egg was a mutation of whatever animal laid it. Let's call it a pre-chicken or precken (pre-kin). So we could say that preckins lay preckin eggs just as chickens lay chicken eggs. But the egg that contained the first chicken ever was laid by a preckin so is that a preckin egg that contains a chicken or is it a chicken egg?