In general, chickens lay most robustly for two years. That is why commercial egg farms will tend to rotate in new pullets every two years, sending the older ones to auction. Or, my cousin who has a small farm will buy new chickens every year and then rotate out half her flock, the older hens, at that time. So she always has new hens and then year old hens, and when the older ones reach two years, she brings in new ones. Does that make sense?
But for a small farmer or someone keeping chickens as pets, you would probably see a drop off in egg production after a couple years, but they still lay. i read about someone on this board with a 13-year-old chicken that was still laying.
i haven't been keeping chickens too long, and my oldest hen is about 3 years. She hasn't laid in a while, but that may just be because it's winter. In any case, she has a home here forever. But i did just add 4 pullets to that pen, as i do like having plenty of eggs.