Wash the chicken and pat dry. Remove the fat. Cut each chicken breast into 5 or 6 slices. Place the chicken slices in a ziplock bag. Gently pound the slices for form medallions, about 2-3 inches in diameter. Dredge each piece in flour. In a large sauté pan, add the olive oil. When the pan is hot, add the chicken strips, making sure they don't overlap. Cook the chicken until it is lightly golden-brown on both sides (about 1-2 minutes per side). Add the Marsala (caution: it may flame up). Turn the heat down to medium and simmer for about 30 seconds. Add butter, yellow onions, green onions, parsley, and mushrooms. Simmer for 2-3 minutes, stirring gently. If the ingredients are too dry, add chicken broth to create a rich and creamy consistency. Add salt and pepper to taste. Serve about 5-6 medallions per serving. Place medallions over a bed of rice. Scoop some of the scallopine sauce over the top. Garnish with parsley.