Preheat the oven to 375°F.
Heat 2 tablespoons of olive oil in a large sauté pan on medium high or high heat. Season the chicken pieces all over with salt and pepper. Brown the chicken pieces on both sides, about 1 to 2 minutes per batch. Remove chicken pieces and set aside in a bowl.
In the same sauté pan add 1 tablespoon olive oil. Lower the heat to medium, add the onions, and cook until translucent, about 3 minutes. Add the garlic; cook 30 seconds more. Remove onions and garlic to a shallow 9 x 13-inch casserole dish.
Raise heat to medium high and add the sliced mushrooms. Dry sauté the mushrooms, allowing them to brown lightly and release some of their moisture. Add the mushrooms to the casserole dish.
Add ¼ cup dry sherry or dry white wine to the pan to deglaze it, scraping off the browned bits from the bottom. Let the sherry reduce to about 1 tablespoon, then add the chicken stock, and remove from heat. Stir in 1 ½ teaspoons salt, the cream, and the sour cream.
Add the uncooked rice to the casserole dish. Then pour the stock, sherry, cream, and sour cream mixture over the rice. Add the Italian and poultry seasonings and paprika to the dish. Stir the rice, onion, mushroom, and herb mixture so that they are evenly distributed in the casserole dish. Place the chicken pieces on top of the rice mixture.
Cover the casserole dish tightly with aluminum foil. Bake in a 375°F oven for 45 minutes and then remove foil. If the casserole still has too much liquid, let it cook a few minutes more, uncovered, until the excess liquid has evaporated away.
Sprinkle with fresh parsley before serving.
