Preheat your grill or oven to medium-high heat.
Season the chicken drumsticks with salt, black pepper, and garlic.
In a bowl, mix together brown sugar, chopped onion, ketchup, white wine vinegar, Worcestershire sauce, and vegetable oil.
Brush the sauce onto the chicken drumsticks, ensuring they’re well-coated.
Grill or bake the chicken for about 30 minutes, turning occasionally and basting with extra sauce.
Once the chicken is golden brown and cooked through, remove it from the grill or oven.
Serve hot with your favorite sides.