Rinse the chicken and pat it dry with paper towels. Remove any giblets if needed. Let the bird come to room temperature for about 20 minutes.
Mix the dry rub ingredients in a small bowl: brown sugar, paprika, salt, pepper, garlic powder, onion powder, and cayenne. This forms a rustic, balanced crust.
Brush the chicken with olive oil, inside and out. Generously rub the dry mix over the skin, pressing it in so it adheres. Don’t forget under the wings and around the cavity for even flavor.
Preheat your smoker to about 250–275°F (120–135°C). If you don’t have a smoker, set up a charcoal grill for indirect heat and use a water pan to keep things moist.
Place the chicken breast side up on the grate. Smoke for about 2.5 to 3 hours, or until the internal temperature reaches 165°F (74°C) in the thickest part of the thigh.
If you like a glaze, brush on a light layer of barbecue sauce during the last 15–20 minutes of cooking. Finish with a few minutes of indirect heat to set the sauce.
Remove from heat and let rest for at least 10 minutes before carving. This helps the juices redistribute.