Preheat oven to 350ºF. Lightly spray a 9x13x2-inch baking dish with cooking spray.
Pour cream of chicken soup, cream of mushroom soup, chicken broth, rice and onion soup mix in bottom of baking dish. Whisk together. (you can do this in a bowl and pour it into the baking dish if you prefer)
Place chicken on top of rice mixture.
Cover tightly with foil and bake for 1 hour 15 minutes to 1 hour 30 minutes.