Whisk all marinade ingredients together and pour into a glass dish or plastic gallon zipper storage bag.
Cut 3 diagonal slits in the top of each breast, about 1/4" deep, to help soak up the marinade. Place the chicken into the marinade, turn to coat. Refrigerate and marinate for a minimum of 1 hour, up to 24 hours.
Remove the chicken from the marinade, and let the excess drip off. Dab gently with paper towels.
Preheat the grill on high, covered, for about 15 minutes. Open lid and brush grate with grill brush.
Turn the grill temperature down to medium-low. Wad up a couple pieces of paper towel and grab the wad with a pair of tongs. Dip the wadded paper towel into some vegetable oil, then using the tongs, brush the grates with the oiled paper towel.
Place the chicken onto the grill and cover with a disposable aluminum pan. Allow to cook for 6-8 minutes, long enough to create nice grill marks. Turn the breasts over and cover with aluminum pan for 6-8 minutes more.
Turn grill temperature back up to high. Grill chicken a few minutes more on each side. Internal temperature should be 165.