In a large skillet, cook the chicken, green peppers and onion in 2 tablespoons oil over medium heat for 6-8 minutes or until chicken juices run clear. Stir in barbecue sauce. Bring to a boil. Reduce heat; simmer for 1-2 minutes or until heated through.
Sprinkle cheese down the center of each tortilla; top with chicken mixture. Fold sides and ends over filling and roll up.
In a large skillet, brown burritos in remaining oil on all sides over medium heat. Serve with lime wedges, sour cream, lettuce and tomatoes if desired. Yield: 4 servings.