In bowl, whisk together all chicken marinade ingredients. Reserve 1/3 cup of marinade in a bowl to use as a salad dressing for later.
Place chicken breasts into a gallon plastic bag, pour remaining marinade over chicken. Seal bag and allow chicken to marinade for 3 hours or overnight.
When chicken has marinaded, heat grill to medium high heat. Let chicken sit out for 30 minutes before grilling.
Grill until just cooked through. Remove from grill and cover with foil. Let rest for 10 minutes.
For Salad: Toss together all shredded vegetables. Plate on four plates, topping with one chicken breast each.
Pour additional reserved marinade/dressing from clean bowl over the top of the chicken. Devour.