This is one of those questions which is supposed to confound evolutionists because it gets to the heart of the matter so quickly.
Chickens lay eggs. Chickens come from eggs. Without the egg, there would be no chicken. Without the chicken there would be no egg.
So which came first? The chicken or the egg.
If the chicken evolved it had to evolve from something. But if that's the case, wouldn't it have evolved from an egg? But the egg already has all of its own genetic material so it couldn't have changed or mutated. It would be in a state of finality...so it can only produce one animal, the chicken. So the chicken couldn't have evolved from an other species only from the egg. And the egg already has all of the genetic material necessary to create a chicken. So the chicken and egg are already in their final states of development. Moreover, they are already in their first state of development. The chicken can only lay chicken eggs, the chicken eggs can only produce chickens. So there is no way that the chicken or egg could have evolved.
That argument only works because it assumes that the egg genetic material cannot be modified. The answer is that it can. There can be many contributing factors that mutate or change the egg. Radiation, external temperature variations, missing genetic cell instructions, protein development that did not work right, RNA carrying instructions that are not fully implemented in creating proteins. And if these variations continue over a long period of time a small instruction change can have large effects over time.
The egg is very fragile from an external point of view, but also internally. The chicken did come from an egg, but the first egg did not come from a chicken. No it came from an animal closely resembling a chicken, but the egg is a genetic mutation. And over a long period of time the egg's genetic material took on a form that we recognize today - the Chicken.
What this means is that over long period of time, there are no static life forms, all have the capacity to mutate and change.
For a different take see: