Preheat oven to 425 degrees F. Skin chicken. Brush chicken with oil; sprinkle the 1 teaspoon pepper and 1/4 teaspoon salt over chicken. Arrange chicken in a 15101-inch baking pan. Bake, uncovered, for 35 to 40 minutes or until chicken is tender and no longer pink (170 degrees F).
Meanwhile, for sauce, in a medium saucepan, cook mushrooms in hot butter until tender. Stir in flour and 1/4 teaspoon salt. Add broth and Marsala. Cook and stir over medium heat until thickened and bubbly; cook and stir for 1 minute more. Pass sauce with chicken. If desired, sprinkle with additional pepper.