Add marinade ingredients to a zipper plastic bag. Add butterflied chicken breast to bag and place in refrigerator to marinate for at least 1 hour (up to 24 hours).
Preheat oven ton 400degF. Remove chicken from bag. Lay flat and open. Place slice of cheese, slice of Prosciutto and 1/3 cup of shredded cheese. Fold chicken over and secure with toothpicks.
Place a cooking rack on a parchment paper covered baking sheet. Lay stuffed chicken breasts on the rack. Bake in oven for 45 minutes. Let cool at least 5 minutes before slicing.