Preheat oven to 350°.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add half of chicken to pan, and cook 2 minutes on each side or until lightly browned. Place on a jelly-roll pan coated with cooking spray. Repeat procedure with remaining chicken. Bake at 350° for 25 minutes or until chicken is done.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add mushrooms, onions, and garlic to pan. Sprinkle flour over the mushroom mixture, and cook for 2 minutes or until flour is lightly browned, stirring constantly. Add 1 cup vermouth to pan, scraping pan to loosen browned bits, and boil for 30 seconds. Add chestnuts, broth, parsley, tarragon, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper; return to a boil. Reduce heat, and simmer until sauce is reduced to 2 cups (about 10 minutes). Add cranberries to pan, and cook for 2 minutes.