First, mix the smoked paprika, garlic powder, onion powder, salt, and pepper in a large bowl. Then add the chicken and toss to coat evenly in the dry rub.
Next, tear four 18x12-inch sheets of heavy-duty foil. Drizzle olive oil in the center. Divide vegetables among sheets, place rubbed chicken on top, drizzle 2 tbsp BBQ sauce per packet. Reserve 1/4 cup sauce for the char-finish.
Bring the long edges of the foil together with a double-fold seam. Crimp short ends to seal. Leave a small air pocket inside. Grill medium-high 20-26 min, oven 400F 25-32 min, or campfire coal bed 30-40 min depending on cut.
At 5 min before done, open each packet carefully. Brush reserved BBQ sauce over chicken. Return open packets to direct grill heat, broiler on HIGH, or coal edge for 3 min until sauce caramelizes. Confirm 165F internal temp.
Rest packets 3-5 minutes. Open carefully away from your face. Garnish with fresh parsley or cilantro. Serve from foil or transfer to plates.
