Wash your hands with soap and water.
Preheat oven to 375 degrees Fahrenheit.
Place a foil sheet, approximately 12x12 inches, on a work surface. Spoon about 1 teaspoon of the barbecue sauce in the center of the foil sheet. Place one chicken breast half over barbecue sauce and spread another teaspoon of sauce over chicken. Top with a quarter of the potato, bell pepper and onion. Sprinkle with a little of the salt and pepper.
Fold foil in half to cover contents; make narrow folds along edges to seal. Repeat with remaining ingredients to assemble three more packets. Place packets on a baking sheet and bake for 35 minutes.
Open foil packets with scissors and carefully pull back edges (contents may be very hot). Sprinkle a quarter of the cheese over the top of each chicken breast half and return to oven, unsealed, for 2 minutes or until cheese is melted. With a spatula, transfer the contents of each packet onto individual serving plates, if desired.