In a small bowl, combine salt, pepper, smoked paprika, garlic powder, onion powder, and brown sugar to create a dry rub.
Pat chicken pieces dry with paper towels, then rub all over with olive oil. Coat evenly with the dry rub.
Place chicken in a large resealable bag or bowl, cover, and refrigerate for at least 2 hours (or up to 24 hours).
Preheat grill to medium-high heat (about 400°F). Create two zones: one direct (hot) and one indirect (cooler).
Grill chicken over direct heat for 2–3 minutes per side to sear and develop grill marks.
Move chicken to indirect heat, cover grill, and cook for 20–25 minutes, turning occasionally, until internal temperature reaches 165°F.
During the last 10 minutes, baste chicken generously with BBQ sauce mixed with apple cider vinegar (if using).
Remove from grill and let rest for 5 minutes before serving.