Add that to the chicken joke from Long Dark Teatime of the Soul*, and you have to wonder if every chicken joke is profound.**
*It was S2, my youngest sister, who brought this to my attention. I think she was in junior high at the time. She shared with me the actual answer to the joke, which was that the bible said that the birds of the air were created all on one day, so that meant that the chicken had come first. I don't think she meant it as a point of personal dogma, she was just pleased to have found an authority to quote on the matter.
I thought it over and decided that, if considered from an evolutionary perspective, there would have been a theoretical moment when a non-chicken produced an egg with the final mutation that resulted in a chicken. Or maybe it would have been too gradual to determine the divide between non-chicken and chicken.
While I was pondering that, I remembered that, again from an evolutionary perspective, eggs had been laid by creatures for millions of years before chickens evolved. I know that's kind of a cheap shot answer, since I'm pretty sure that the joke is referring to chicken eggs, not fish or amphibian or reptile ones, but I liked the reference to authority and I liked it's symmetry with my sister's answer.
Conceivably, if everyone realized that there was a creationist answer and an evolutionary answer, one could ask the riddle and use the answer to see if the questionee was one of us or one of them.
**First Person: "We're terribly worried about Uncle Henry. He thinks he's a chicken."
Second Person: "Well, why don't you send him to the doctor?"
First Person: "Well, we would only we need the eggs."