Combine first 5 ingredients in a small saucepan. Season lightly with salt and pepper and bring to a boil over high heat. Reduce heat to low, simmer until peaches are very soft and flavors meld, about 10 minutes. Remove pan from heat; let cool. Pour peach mixture into a blender and purée until smooth. Season to taste with salt and pepper. Place half the sauce in a medium bowl; add the chucked and turn to coat. Let marinate at room temperature for 20 minutes. Cover and refrigerate remaining sauce.

Prepare a grill to medium-high heat. Brush grill rack with oil. Grill chicken until browned and almost cooked through, 4-5 minutes per side. Brush on all sides with reserved sauce; grill until glazed and cooked through, 1-2 minutes per side. Slice crosswise. Serve remaining sauce alongside. 4 servings