Originally Posted by Martian

First of all, let's clarify the question. It's not 'the chicken or the egg,' but rather 'the chicken or the chicken egg.' Perhaps a semantic distinction, but given that pretty much all reptiles, arthropods and a even a couple of mammals are oviparous, it's important.

Originally Posted by Martian

That said, it's fairly simple to determine that the egg must've come first. If we had a perfect fossil record and were able to trace the genetic ancestry of the modern chicken back through time, we would eventually hit a point where we'd find what's called speciation. Things do get a bit hazy here, because evolution is a continual and gradual process; however, at some point along the ancestral chicken line we would be obliged to draw a line where we can say that everything after it is a chicken, and everything prior to it is not. Where this line falls is immaterial, because we're only really concerned with the mechanism. Once we've isolated that population that can be considered chickens from that other population that comprises the pre-chickens, we can then identify the group of individuals that we would consider the first chickens.

Once we've done that, it's very easy to answer your question. An entity is genetically distinct from it's parents from the moment of conception. Once that sperms meets that ovum and the DNA synthesis occurs, we have a zygote that carries DNA which shares common traits with both parents, but is distinct from either. And there's our egg. Now, the chicken has to have hatched from an egg much like this one, and the organisms on the other side of our line are by the definition we've established not chickens, since they're pre-chickens. Therefore, the egg that will hatch into a chicken necessarily predates the chicken itself (they're the same entity in two forms) and the organisms that made the egg are not chickens. The egg came first.