Preheat grill to medium-high heat (about 375°F). If using oven, preheat to 400°F.
Pat chicken dry with paper towels. Season all over with salt and pepper.
In a small bowl, mix barbecue sauce, apple cider vinegar, brown sugar, smoked paprika, and garlic powder. Set aside half of the sauce for serving.
Grill chicken skin-side down for 5-7 minutes until grill marks form. Flip and cook another 5 minutes.
Brush chicken generously with sauce. Continue grilling, turning and basting every 5 minutes, until internal temperature reaches 165°F, about 20-25 minutes total.
Remove chicken from grill, let rest 5 minutes. Serve with reserved sauce.
Tips
For oven method: Place chicken on a foil-lined baking sheet, bake 25 minutes, then brush with sauce and bake 10 more minutes.
Letting the chicken rest before serving helps retain juices.