Sprinkle chicken evenly with 1/8 teaspoon each salt and pepper. Place chicken on grill rack coated with cooking spray; grill 5 to 7 minutes on each side or until done.
Combine spinach, grapes, and sesame seeds in a large bowl. Combine vinegar, grape juice, sesame oil, and remaining salt and pepper.
Slice chicken diagonally into thin slices. Toss chicken with spinach mixture. Drizzle vinaigrette over salad.