Preheat grill on high heat for 10 minutes, then turn off one side (gas grill) or bank coals to one side (charcoal). This creates a hot direct heat side and a cooler indirect heat side. Oil the grates well to prevent sticking.
Place chicken skin-side down on the cooler, indirect side of the grill, then cover and grill for 30–40 minutes, turning occasionally to prevent burning and ensure even cooking. Be sure to maintain a medium to medium-high (about 350–400°F) temperature and rotate every 10-15 minutes.
Move chicken to the hot, direct side of the grill, and place skin-side down to crisp up the skin. Brush with BBQ sauce, cook 2–3 minutes, flip, baste again, and repeat for 2–3 cycles until nicely caramelized, and watch out for burning. Due to the high sugar content, BBQ sauce can easily burn, so wait to baste in the last 10–15 minutes.
Remove chicken when it reaches 160–165°F. Carryover heat will finish the cooking as it rests. Let the chicken rest, loosely tented with foil, for 5–10 minutes before serving. This keeps it juicy as the juices redistribute.
Enjoy with extra BBQ sauce and a few of your favorite sides!