1. Combine 1/2 cup balsamic vinegar, garlic, and chicken in a freezer bag. Cover and marinate in refrigerator (1 hour).
2. Remove chicken from freezer bag and discard marinade. Place chicken on broiler pan coated with cooking spray and broil on high on the top rack, turning once, until chicken reaches a minimum internal temperature of 165 degrees F (5-6 minutes per side).
3. Toss remaining 1/4 cup balsamic vinegar with salad greens. Serve greens topped with chicken.