Pat chicken quarters dry with paper towels and place in a large bowl. Whisk together smoked paprika, garlic powder, onion powder, black pepper, salt, brown sugar, and cayenne pepper in a small bowl. Drizzle olive oil, Worcestershire sauce, and liquid smoke over the chicken.

Rub the spice mixture thoroughly over all sides of the chicken, ensuring each piece is evenly coated. Squeeze fresh lemon juice over the coated chicken and scatter thyme on top, pressing gently so it adheres. Let rest at room temperature for 10 minutes while prepping your grill.

Preheat your grill to medium-high heat (400°F), ensuring grates are clean and lightly oiled to prevent sticking. Place chicken quarters skin-side down on the grill, arranging them so they don't touch.

Cook for 15-18 minutes without moving, allowing the skin to crisp and develop beautiful char marks. This initial sear locks in juices and builds the foundation for our smoky grilled BBQ chicken quarters recipe's signature crust.

Flip quarters carefully using tongs and reduce heat to medium. Brush generously with BBQ sauce and cook for 12-15 minutes until internal temperature reaches 165°F at the thickest point.

During the final 2 minutes, brush chicken with a second coat of sauce, creating a glossy caramelized finish. Transfer to a clean platter and let rest for 5 minutes before serving to retain maximum juiciness.