Place 1 piece of chicken, boned side up, between 2 pieces of clear plastic wrap. Working from the center to the edges, pound lightly with a meat mallet to about 1/4-inch thickness. Remove plastic wrap. Repeat with remaining chicken breast halves.
Spray a large skillet with nonstick spray coating. Preheat skillet over medium heat. Add 2 chicken breast halves. Cook over medium heat for 2 to 3 minutes or until tender and no pink remains. Transfer to a platter; keep warm. Repeat with remaining chicken breast halves.
Carefully add mushrooms, green onion, water, and salt to skillet. Cook over medium heat until mushrooms are tender and most of the liquid has evaporated (about 3 minutes). Add Marsala or dry sherry to skillet. Heat through. Spoon vegetables and sauce over chicken. Makes 4 servings.