Prepare the marinade by combining the ingredients needed into a jar or measuring cup. Stir to combine.
Add the chicken to a large sealable container or plastic bag.
Pour the marinade over the top, seal and place in refrigerator to marinate for at least 30 minutes, preferably for 4–6 hours.
Set up two zone grill by placing charcoal on one side, or if using gas grill, turn all burners to high, cover and heat the grill then leave on the primary burner and turn off the others. Preheat grill to 400-425 degrees F.
Remove the chicken from the marinade, discard the marinade. Pat the chicken dry using a paper towel.
Place drumsticks, skin side down on the indirect heat zone on the grill. Cover and cook 15-20 minutes. Rotate chicken to allow chicken further from the heat to be closer, and vice versa.
Close lid and continue cooking another 15 minutes or until chicken registers approximately 160 degrees F.
With the lid open, place the chicken over the direct heat and cook until chicken has nice grill marks, approximately 4-5 minutes per side.
Check the internal temperature and removing from the grill once chicken reaches 185-190 degrees F.
Let rest for 5 minutes covered loosely with foil, then serve.