According to the theory of evolution, chickens evolved from earlier bird species through a process of natural selection over millions of years. Therefore, it is likely that the first "chicken" was not born as a fully formed chicken but rather as a result of genetic mutations that gradually occurred over time.
In other words, at some point in the evolutionary process, a bird species that was not quite a chicken laid an egg that contained the genetic mutation that would eventually lead to the first true chicken. So, technically speaking, the egg came first, and the first true chicken hatched from it