Preheat your oven to 350°F.
In a large mixing bowl, combine the shredded rotisserie chicken, cream of celery soup, cream of chicken soup, sour cream, and poppy seeds. Stir until everything is smooth and evenly combined. The mixture should be thick and creamy.
In a separate bowl, mix the crushed Ritz crackers with the melted butter. Stir until all the crumbs are evenly coated. This step ensures the topping bakes up golden and crisp rather than dry.
Sprinkle half of the buttered cracker mixture evenly into the bottom of a 9x13 baking dish.
Spread the chicken mixture evenly over the cracker layer, smoothing it out with a spatula.
Top with the remaining Ritz cracker mixture, distributing it evenly across the surface.
Cover the dish with foil and bake for 20 minutes.
Remove the foil and bake for an additional 15 minutes, or until the casserole is bubbly around the edges and lightly golden on top.
Let the casserole rest for a few minutes before serving to allow it to set slightly.