Can you leave chicken in smoker after it quits cooking to stay warm
Safety-wise, as long as you keep the chicken above 140°F, you can keep it there forever. Once you get below 140°F, you're supposed to have it either eaten or cooled to 40°F within 2 hours. (It's actually safe a little lower—but it's best to leave a margin of error!) For details, see How do I know if food left at room temperature is still safe to eat?

Quality-wise, it's going to continue to cook, and its going to continue to lose moisture (unless your smoker is really humid, like a commercial combi oven can be). The hotter it is, the faster it will cook and dry out. Cooking is fairly slow once you get down to near 140°F, though.

Three hours should be doable.