1 3 1/2–4-lb. chicken, cut into 10 pieces (breasts halved)
2 tablespoons Spice Rub
Spice Rub (combine all)
4 tablespoons kosher salt
3 tablespoons brown sugar
2 tablespoons sweet paprika
1 tablespoon cayenne pepper
Heat oil in a medium saucepan over medium heat. Add tomato paste and cook, stirring often, until paste turns brick-red, about 2 minutes. Add garlic powder, onion powder, paprika, cayenne, and black pepper. Cook, stirring, until fragrant, about 1 minute. Add vinegar, orange juice, brown sugar, molasses, Worcestershire sauce, mustard powder, and 3 cups water. Cook, stirring occasionally and scraping up any browned bits, until reduced by half, 50–60 minutes; season with salt.
Prepare grill for medium heat. Season chicken with Spice Rub. Grill, turning occasionally, until lightly charred, 15–20 minutes. Continue grilling, turning and basting with barbecue sauce often, until chicken is cooked through and an instant-read thermometer inserted into the thickest part of thigh registers 165°, 8–10 minutes longer.