Over the years you've probably had your share of barbecued chicken legsdrumsticks cooked on the grill, coated with sauceand some may have been better than others. Once you taste this recipe, though, it will be the only one you will use when making barbecue chicken on the grill. These drumsticks are brined first to create optimal moisture and tenderness, and then are slowly grilled and basted with a classic BBQ sauce at the end of cooking time. While this recipe contains ingredients for making a homemade sauce, feel free to use your favorite bottled sauce if you prefer.