Make four foil packets by the following method, using 1-foot squares of heavy duty aluminum foil: fold square in half and smooth flat. Seal each of the narrow ends by folding over each edge three times to make a 1/4-inch border, smoothing flat after every fold. You should now have a foil packet that is open on one long side. Repeat to form four packets.
In a bowl or resealable plastic bag, combine the potatoes, chicken cubes, red peppers, onion, celery, and barbeque sauce; mix well. Evenly divide the mixture among the foil packets. Roll up the open end of the packets to seal.
Place packets on a grill over the coals of a fire. Cook until the potatoes are tender and the chicken is fully cooked, about 25 minutes, depending on the intensity of the heat.