Heat the oven to 375°F and grease a 9-by-13-inch baking dish with the vegetable oil.
Stir the rice, soup, water, mushrooms and half the onion soup mix together in the dish.
Set the chicken breasts in a single layer over the rice and season them with the pepper, paprika and remaining onion soup mix.
Cover the dish tightly with foil and bake for 55 minutes without opening it.
Remove the foil and bake for 10 to 20 minutes more, until the rice is tender and the thickest chicken breast reaches 165°F.
Rest the covered casserole for 10 minutes, then stir the rice around the chicken before serving.