Preheat the oven to 350 degrees F. Butter a casserole dish and set aside.
Heat the oil in a large skillet over medium-high heat. Add the onions and cook until beginning to soften, 2 to 3 minutes. Add the mushrooms and cook until golden, about 4 minutes.
Sprinkle the chicken liberally with salt and pepper. Push the onions and mushrooms to the side of the skillet, add the chicken skin-side down and and cook until the skin is browned, about 4 minutes. Remove the chicken to a plate.
Stir the rice into the onion and mushroom mixture and cook for 1 minute. Stir in the wine, bring to simmer and simmer for 1 minute. Stir in the soup and 1 1/2 cans of water and bring to a simmer.
Pour the rice mixture into the buttered casserole dish. Place the chicken on top skin-side up and cover with a lid or foil. Bake, stirring in more water 1/2 cup at a time if the casserole starts to dry out, until the rice is tender, about 30 minutes.