Sprinkle onion soup mix in the bottom of a 9x13-inch baking dish. Spread rice over soup mix and place chicken on top of rice. Combine chicken broth, cream of mushroom soup, and cream of celery soup in a bowl. Pour soup mixture over chicken and rice; cover dish with aluminum foil.
Bake in preheated oven until chicken is no longer pink in the center and juices run clear, about 1 hour. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
