Preheat the grill to medium heat. Lay out 4 (12″) sheets of non-stick foil (or spray with non-stick spray). Place one chicken breast on top of each piece. Salt and pepper. Then spread about 2 Tablespoons of BBQ sauce onto each piece. Divide the green beans, bell pepper and onion among the 4 sheets. Add more salt and pepper on top of the vegetables if desired. Cover the top with foil and fold in the sides so the packets are secure.
Place each packet on the grill. Cook for about 20 minutes (or until the chicken is cooked through), flipping at about 12 minutes. Brush with more BBQ sauce if desired.
Allow packets to rest for a couple minutes off the grill. Serve while warm on plates.
These packets can also be cooked in the oven. Preheat oven to 400°F and then bake for 22 minutes, or until the chicken is cooked through. Remove the top sheet of foil and then broil for an additional 2-3 minutes.