- Preheat half of the barbecue to high and the other half to low. Oil the grate.
- In a large bowl, whisk together all of the ingredients except the chicken. Season with pepper. Add the chicken and toss to coat well in the marinade.
- Place the drumsticks on the side of the grill set to low. Close the lid and cook for 30 minutes, turning the drumsticks over several times. Set the marinade aside.
- Meanwhile, in another bowl, combine all of the ingredients. Let marinate while you cook the chicken.
- Brush the chicken with the reserved marinade. Transfer to the side of the grill set to high and cook for 5 minutes or until the chicken is cooked through and nicely browned.
Serve with pieces of grilled corn on the cob, if desired.