Prepare Sherry Vinaigrette; set aside 1/4 cup vinaigrette.
Coat peach halves and chicken with cooking spray; brush chicken with remaining 1 1/2 tablespoons vinaigrette. Place peach halves and chicken on a grill rack coated with cooking spray. Grill chicken 3 to 4 minutes on each side. Grill peach halves 1 to 2 minutes on each side; cut each half into 4 wedges.
Cut chicken crosswise into thin strips. Place peach wedges, chicken strips, spinach, and pine nuts in a large bowl; drizzle with reserved 1/4 cup vinaigrette, and toss well. Place 2 cups salad mixture on each of 4 plates; sprinkle evenly with cheese.