Egg, no question.
Eggs first formed in species that existed millions of years before chickens, so eggs well predate chickens.
The first creature we would recognise as a chicken would have emerged from an egg.
Ben has it right. Over a long period of time, animals changed slightly until a chicken emerged from the egg. The animal that laid the egg that hatched the chicken? It would have looked similar to a chicken, but wasn't quite there yet. It would be like how a dog that is half border collie half german shepherd wouldn't look exactly like a german shepherd, or a border collie, but you could see the resemblance.
Even the first chicken wouldn't have looked like the chickens we have now. Because we have cultivated them and manipulated their evolution, they have changed quite significantly.
But going back far enough, there would be an animal that didn't lay eggs. That animal would look very different from a chicken. Eventually there were reptiles that started laying eggs, then those reptiles' offspring eventually popped out with feathers. After a long period of time, a chicken popped out.
Conclusion: the egg came first, and it came out of something that wasn't a chicken.