Q: What came first, the chicken or the egg?
Answer 1: Chicken
In asking 'what came first' it is implied that one or the other did actually come first. I'll go with that. If one of these did in fact come first, then it would have been the first, and since we've had both chickens and eggs for as long as mankind can remember, it's a safe bet that the first one appeared a LONG time ago. Our environment today isn't really a safe haven for chickens, and I can't see the world being a safer place back when the first egg or chicken appeared.
This question is also kind of saying there was a cosmic, divine, or otherworldly 'tada!' moment eons ago when the first egg/chicken came into being. Otherwise you have to account for evolution which would make this question just stupid, and this is not a stupid question.
So we have a egg/chicken suddenly appearing in a hostile world a long long time ago. If it was the egg, it would have to eventually hatch and mature in order to propogate the species. I'd say it would have had a snowball's chance at surviving. True, the chicken probably wouldn't fare much better, but being 'poofed' into existence already mobile does give it a running chance at success.
Answer 2: Egg
Eggs are traditionally a breakfast food, while chicken is reserved for those later meals. Hence, eggs come first (fried, well-done), then the fried chicken.
Answer 3: Egg
Once again I am taking liberties in decifering the meaning of the original question. 'What came first' assumes they came from somewhere. Coming from someplace implies travel of some sort. Since the question only asks about which one was first, there's no reason to assume they didn't both arrive together, just that one came first.
Now, if there was travel involved, then we can say that due to the awkwardness of chickens in general (till they are cooked anyway), and the aerodynamic shape of the egg, the egg would clearly be able to go faster than the other (assuming they both had the same source of propulsion).