- In a small saucepan over medium-high heat, bring balsamic vinegar to a boil; reduce heat and let simmer until the vinegar is reduced by 1/2, approximately 20 to 25 minutes. Stir in molasses and black pepper. Remove from heat and set aside.
- In a medium bowl, combine basil, garlic, and olive oil. Rub chicken breasts with the basil mixture; sprinkle with salt and pepper.
- Preheat barbecue grill (spray grill with vegetable-oil cooking spray). Place chicken onto hot grill and brush with balsamic vinegar glaze. Cover barbecue with lid, open any vents, and cook 20 to 25 minutes until done.
- Just before 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 chicken and peaches from the grill, transfer onto a serving platter, and serve immediately.
NOTE: Peaches may be served whole or sliced with the chicken breasts.