Rinse the chicken thoroughly under cold water, then pat it dry with paper towels. Trim any excess fat and the wing tips, if necessary.
In a small bowl, combine the salt, pepper, garlic powder, smoked paprika, and brown sugar. This will be your dry rub.
Drizzle the chicken inside and out with olive oil, then generously sprinkle with the spice mixture. Massage it in to ensure even coverage.
Preheat your grill to medium heat (about 350°F or 180°C). If using a charcoal grill, create an indirect heat zone for slow cooking.
Place the chicken breast-side up on the grill grate and cook for 45-50 minutes, turning occasionally for even cooking.
In a small bowl, combine the apple cider vinegar and Worcestershire sauce. Start basting the chicken with this mixture during the last 20 minutes of grilling.
During the last 10 minutes, brush the chicken with BBQ sauce and continue grilling until the glaze is slightly caramelized on the skin.
Remove the chicken from the grill and let it rest for at least 15 minutes before carving. This allows the juices to redistribute, keeping the meat succulent, and allows the flavors to meld.
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