In a large skillet, over medium heat, cook chicken, green pepper and onion in 2 tablespoons of oil for 6 to 8 minutes or until chicken juices run clear.
Stir in barbecue sauce and bring to a boil. Reduce heat and simmer for 1 to 2 minutes or until heated through.
Sprinkle cheese down center of each tortilla and top with chicken mixture. Fold sides over first, then fold ends over and roll up.
In a large skillet, over medium heat, brown burritos in remaining oil on all sides.
Serve with lime wedges, sour cream, shredded lettuce and chopped tomatoes if desired.