Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13-inch baking dish.
Stir cream of chicken soup, cream of mushroom soup, and rice in a large bowl. Mix hot water and chicken bouillon in a bowl until bouillon is dissolved; stir into rice mixture. Spread rice mixture into prepared baking dish and sprinkle with half the onion soup mix. Sprinkle remaining onion soup mix over chicken breasts; arrange chicken in a single layer over rice mixture. Cover with aluminum foil.
Cook the chicken breasts until no longer pink in the center and the juices run clear, 2 1/2 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).