In a medium bowl, combine the ketchup, apricot nectar, brown sugar, chutney, vinegar, Worcestershire sauce, Cajun seasoning, and hot-pepper sauce (if using).
Warm the oil in a medium nonstick skillet over medium heat. Add the onions and red peppers. Cook, stirring often, for 5 minutes, or until the onions are translucent. Stir in the mangoes and cook for 5 minutes. Stir in the ketchup mixture and simmer for 10 minutes, or until slightly reduced.
Coat a grill rack or broiler pan with nonstick spray. Preheat the grill or broiler.
Season the chicken with the salt and black pepper. Cook 4" (11 cm) from the heat for 4 to 5 minutes, or until browned. Turn the chicken over and brush the cooked surface with some of the sauce. Cook for 4 to 5 minutes, or until no longer pink in the center when tested with a sharp knife. Turn over again, brush with more of the barbecue sauce, and cook for 1 minute. Serve drizzled with the remaining sauce.