Cover a clean plastic cutting board with a large piece of plastic wrap. Place one chicken breast on top of it, and cover with another large piece of plastic wrap. You can also use resealable freezer bags for this job. Using a kitchen mallet or rolling pin, gently hit to flatten chicken breasts working from the thickest portion in the middle to the outer edges. Flatten each breast to a uniform thickness of a half of an inch.
Combine sauce/marinade ingredients. Separate half of it to use as the sauce (store in the refrigerator until ready to use, and the remaining half as the marinade. Place breasts into a resealable plastic bag and pour the marinade portion over top, making sure that all surfaces are well coated. Seal bag and place into the refrigerator for 2-4 hours.
Preheat your grill for medium heat. Since the breasts have been flattened, they will not take as long to cook. So, stay close to the grill, and keep the reserved sauce nearby.
Remove chicken from bags and place them onto a large plate. Season with a little salt and black pepper on both sides. Place breasts on to grill grate and cook for 4-5 minutes, turn, and brush cooked side with reserved sauce. After 3 more minutes, turn breasts and brush more sauce on. Continue cooking until the internal temperature of each breast reaches at least 165 degrees F.
Once cooked through, remove from heat and place onto a clean platter or cutting board. Slice breasts into desired sizes and use them in your favorite dishes.
Refrigerate chicken breasts in an airtight container for up to 4 days in the refrigerator, or freeze for 3-4 weeks.