In medium bowl, mix barbecue sauce, minced onion and cola beverage. Divide barbecue sauce mixture evenly into 2 (1-gallon) resealable food-storage plastic bags. Add 6 chicken breasts to each bag; seal bags and turn to coat. Refrigerate at least 6 hours or overnight to marinate, turning bags once or twice.
When ready to cook chicken, heat gas or charcoal grill. When grill is heated, carefully oil grill rack. Remove chicken from marinade; reserve marinade. Place chicken on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 12 to 15 minutes, turning occasionally, until juice is no longer pink when centers of thickest pieces are cut and thermometer inserted in centers reads 170°F.
In 1-quart saucepan, heat remaining marinade to boiling. Serve chicken with sauce.