That assumption is the theory of evolution. If you take evolution to be true, then the following follows: As with every known modern life form, there was an immediate precursor to the modern chicken as we know it today. Call it Chicken-1. Chicken-1, one day, after hundreds of thousands of years, laid an egg that contained a baby with mutated DNA, in other words, the DNA of modern chickens. And from that egg, came the chicken (modern chicken). So the egg came first.