Preheat oven broiler. Arrange peppers on roasting pan. Place under hot broiler, about 5 inches from heat; cook till skin turns black. Turn frequently to char all sides. Remove peppers from roasting pan and place in a plastic bag. Close tightly and allow to steam 10 minutes. Cook rice according to package directions. When rice is done, remove from heat and keep warm. Carefully remove peppers from bag. When peppers are cool enough to handle, slip off and discard charred skins. Hold peppers under cold running water to make peeling easier. Chop peppers coarsly. In work bowl of food processor, combine peppers with 1 cup heavy cream. Process until smooth. Stir in remaining cream; set aside. Heat vegetable oil in large skillet over med-high heat. Cook chicken breasts until brown on both sides. Season to taste with salt and pepper. Pour cream mixture over chicken. When mixture comes to a boil, reduce heat to a vigorous simmer. Cook until sauce is reduced and slightly thickened, about 20 to 30 minutes. Adjust seasoning to taste. Right before serving, peel and thinly slice avocados. Remove chicken breasts from heat and stir sour cream into sauce. Serve chicken breasts over rice with plenty of sauce and garnish with avocado slices. Makes 6 servings.