Yes, my science can explain this. Evolution in a sentence: during reproduction, DNA copying is never 100% accurate and so children are often differentiated from their parents by small changes or mutations in their DNA—and over a long enough period of time, new species evolve from chains of these mutations.
With this in mind, the first chicken must have hatched from a chicken egg, but that egg must have come from a slightly different species—almost, but not quite, what we would call chickens. So, two-non-chicken parents of an egg laying species created an egg, and thanks to small genetic mutations, a chicken was born. This mutation was probably very subtle, but it was enough to fulfil our criteria for what a chicken is.
Now you can unleash your science during discussions about this ancient question, and correctly answer: the egg.