In a small bowl, combine the chili powder, salt, black pepper, garlic powder, smoked paprika, onion powder, and cayenne if using.

Pat the chicken drumsticks thoroughly dry with paper towels. This helps the skin brown more effectively on the grill.

Drizzle the chicken with olive oil and sprinkle the spice mixture evenly over all sides. Toss or rub gently until every drumstick is well coated.

For a gas grill, preheat to medium-high heat, about 400°F.

Place the drumsticks on clean, lightly oiled grill grates. Cook over medium-high heat for several minutes, turning every few minutes until the skin is browned on all sides.

Reduce the grill to medium-low heat, about 300°F. Close the lid and continue cooking for about 25 minutes, turning once halfway through.

For a charcoal grill, create two cooking zones by arranging most of the hot charcoal on one side. Start the drumsticks over direct medium-high heat and turn them every few minutes until browned.

Move the chicken to the indirect, lower-heat side. Cover and cook for about 25 minutes, turning once halfway through.

Brush the Grilled Chicken Drumsticks generously with BBQ sauce during the final stage of cooking.

Check the thickest part of the drumsticks with an instant-read thermometer. The chicken should reach at least 165°F (74°C).

Remove from the grill and serve hot with extra BBQ sauce if desired.