Remove chicken from the fridge and pat every surface completely dry with paper towels, including under the skin. Let it rest at room temperature for 15–20 minutes before seasoning.
In a small bowl, combine the smoked paprika, garlic powder, onion powder, brown sugar, black pepper, salt, cayenne pepper, and dried oregano. Stir until evenly mixed with no lumps.
Drizzle olive oil over the chicken and rub to coat, then press the dry rub firmly onto all surfaces of each piece, including under the skin where possible. For best results, refrigerate seasoned chicken for 1–4 hours before grilling.
In a small saucepan over medium-low heat, combine the BBQ sauce, honey, apple cider vinegar, and Worcestershire sauce. Heat for 3–4 minutes, stirring occasionally, until warmed and slightly thickened. Divide into two portions — one for basting, one for serving.
Preheat grill to medium heat (375°F / 190°C) and set up a two-zone fire — direct heat on one side, no heat on the other. Lightly oil the grates using a folded oiled paper towel held with tongs.
Place chicken skin-side up on the indirect heat zone, close the lid, and cook for 25–30 minutes, flipping once halfway through, until the internal temperature reaches approximately 150°F (65°C).
Move chicken to the direct heat zone skin-side down, brush the top with BBQ glaze, and grill for 3–4 minutes per side, basting with each flip, until the sauce caramelizes. Watch closely to prevent burning.
Remove chicken when the internal temperature reads 165°F (74°C) for breasts, or 170–175°F (77–79°C) for thighs and drumsticks. Tent loosely with foil and rest for 5 minutes before serving.
Arrange chicken on a platter, brush with a final layer of the reserved BBQ glaze, and serve immediately with remaining sauce on the side.