If you prescribe to the theory of evolution, then this object wins the debate. After all, what came before the egg wasn’t technically a chicken, but something similar yet different. So, the egg would have come first, to then hatch the first chicken.
Of course, the real question here is whether chickens evolved, or whether they were created by the gods? No god claims to have created the first chicken, nor, indeed, the first egg, but they never deny it when asked.
So, which came first? The god or the egg?