To make the marinade: In a medium bowl whisk together the marinade ingredients.
Rinse the chicken breasts under cold water and pat dry with paper towels. Place in a large, resealable plastic bag and pour in the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place in a bowl, and refrigerate for 4 to 6 hours, turning occasionally.
Remove the breasts from the bag and discard the marinade. Grill, bone side down, over Indirect Medium heat until the juices run clear and the meat is no longer pink at the bone, 30 to 40 minutes. For crisper skin, grill the breasts, skin side down, over Direct Medium heat during the last 5 minutes of grilling time. Serve warm.