In a small saucepan over medium-high heat, bring the balsamic vinegar to a boil; reduce heat and simmer until it is reduced by half, approximately 20 to 25 minutes. Stir in the molasses and black pepper. Remove from heat and set aside.
In a medium bowl, combine the basil, garlic, and olive oil. Rub the chicken breasts with the basil mixture; sprinkle lightly with salt and black pepper.
Preheat the grill (spray grill with cooking spray). Place the chicken onto hot grill and brush with balsamic vinegar glaze. Cover the grill with the lid, open any vents, and cook 10 to 15 minutes or until a meat thermometer registers an internal temperature of 165°F. (Juices will run clear when cut with the tip of a knife); turning and basting several times. Grill time is totally dependent on how thick your chicken breasts are.
Just before the chicken is fully cooked, place the peaches on the grill (cut side down). Brush the top side of the peaches with the balsamic glaze. Grill until they are lightly browned, approximately 2 minutes. Turn them over, brush the cut side with the balsamic glaze and continue to cook for another 2 minutes.
Remove the chicken and peaches from the grill, transfer onto a serving platter, and serve immediately.
