Place chicken breasts between 2 pieces of wax or parchment paper and, using a meat mallet, pound to an even ½-inch thickness. (Skip this step if substituting chicken tenderloins.)
Mix all ingredients except chicken together in a small bowl or measuring cup. Place pounded chicken breasts inside a 1 gallon zip-lock bag. Add marinade to the bag, press air out and seal shut. Massage marinade into the breasts until evenly coated. Place the bag in a bowl in the refrigerator (to protect against leakage), and let the chicken marinate in the fridge for at least 5 hours or overnight.
Clean grill and preheat to high. Place chicken breasts on grill, spooning marinade over top. Grill, covered, for 2-3 minutes per side. Do not overcook.