Mix the marinade: In a large bowl, whisk olive oil, vinegar or lemon juice, soy sauce, Worcestershire, smoked paprika, garlic powder, onion powder, salt, pepper, and cayenne.
Marinate the chicken: Pat chicken dry. Add to the bowl and toss to coat.
Cover and refrigerate for at least 30 minutes, and up to 12 hours. For boneless breasts, marinate 30–60 minutes max to avoid mushy texture.
Make the barbecue sauce: In a small saucepan, combine ketchup, brown sugar, vinegar, Worcestershire, mustard, smoked paprika, garlic powder, and chili powder. Simmer over low heat for 5–8 minutes, stirring, until glossy and slightly thick.
Season with salt and pepper. Set aside.
Choose your cooking method: Grill: Preheat to medium (about 375–400°F). Oil the grates.
Oven: Preheat to 425°F.
Line a sheet pan with foil and place a wire rack on top if you have one.
Stovetop: Heat a large skillet over medium and add a thin film of oil.
Cook the chicken to near-done: Grill: Place chicken skin-side down. Cook 6–8 minutes per side for bone-in pieces, until nicely browned and about 150–155°F internal.
Oven: Arrange skin-side up on the rack or pan. Roast 25–30 minutes for bone-in pieces, until 150–155°F internal.
Stovetop: Sear skin-side down 6–7 minutes until deeply browned.
Flip and cook another 5–7 minutes, adjusting heat to avoid burning, until 150–155°F internal.
Sauce and finish: Brush chicken generously with barbecue sauce. Increase heat briefly for caramelization: Grill: Move to hotter side or raise heat. Cook 2–3 minutes per side, basting and flipping once, until sauce is sticky and chicken reaches 165°F.
Oven: Brush with sauce and return to the oven for 5–8 minutes.
For extra char, broil 1–2 minutes at the end.
Stovetop: Lower heat to medium-low, brush with sauce, cover for 2–3 minutes, then uncover and let it bubble to a sticky glaze until 165°F.
Rest and serve: Let the chicken rest 5 minutes. Brush with a little extra sauce and garnish with parsley or scallions if you like. Serve with cornbread, slaw, or grilled corn.