Preheat the grill to 425°F (220°C). Cut four sheets of heavy-duty aluminum foil, approximately 12×18 inches each.
Cut the boneless chicken thighs into bite-size pieces about 1–1½ inches in size.
Cut the Yukon Gold potatoes into approximately 1-inch chunks. Slice the green bell pepper and red onion.
Place the chicken in a large mixing bowl. Add ½ cup of BBQ sauce, vegetable oil, smoked paprika, garlic powder, onion powder, black pepper, and salt.
Toss thoroughly until every piece of chicken is evenly coated in the smoky barbecue mixture.
Add the potatoes, bell pepper, and red onion. Toss again until the vegetables are lightly coated with the sauce and seasonings.
Divide the chicken and vegetable mixture evenly among the four sheets of foil, placing each portion in the center.
Bring the short sides of each sheet together and fold the seam over twice. Fold and tuck the remaining ends securely to create sealed BBQ Chicken Foil Packs, leaving a little room inside each packet for steam to circulate.
Place the packets on the preheated grill and cook for 20–25 minutes, carefully flipping them once halfway through cooking.
Check that the chicken has reached a safe internal temperature of 165°F (74°C) and that the potatoes are easily pierced with a fork.
Carefully open each packet away from your face, as hot steam will escape. Brush or spoon the remaining ¼ cup BBQ sauce over the chicken and vegetables.
Serve immediately while everything is hot and tender.
Oven Method: Place the sealed packets on a baking sheet and bake at 425°F (220°C) for approximately 25–30 minutes, or until the chicken reaches 165°F (74°C) and the potatoes are tender.