Cook Rice A Roni according to package directions. Add the carrots, green bell peppers, and onion in the last 5 minutes of cooking.
Preheat oven to 350ºF. Grease a 9x13 baking dish.
Stir in the cream soup, sour cream, cooked chicken, and black pepper. Remove from heat.
Transfer the mixture, spreading evenly in the baking dish. Cover with cheese.
Bake uncovered for 30 minutes, then serve.