Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Add 1/2 cup onion, and sauté 4 minutes. Combine onion, prosciutto, cheese, breadcrumbs, and 1 teaspoon rosemary in a bowl. Stir well; set aside.
Cut a horizontal slit through thickest portion of each chicken breast half to form a pocket. Stuff about 3 tablespoons onion mixture into each pocket.
Heat 1/2 teaspoon oil in skillet over medium-high heat. Add chicken; sauté 6 minutes on each side or until chicken is done. Remove chicken from skillet. Set aside; keep warm. Add 1/4 cup onion to skillet, and sauté 3 minutes. Add 1/2 teaspoon rosemary, broth, wine, and garlic, and bring to a boil. Cook 5 minutes or until reduced to 3/4 cup. Return chicken to skillet; cover and simmer 2 minutes or until thoroughly heated. Serve sauce with chicken. Garnish with fresh rosemary, if desired.