1. In a shallow dish, combine flour, salt, and pepper. Dip chicken into seasoned flour to coat lightly.
2. In a large frying pan, melt butter over medium-high heat. Cook half of chicken, turning once, until white throughout, about 5 minutes. Remove to a plate. Repeat with remaining butter and chicken.
3. Add shallots to pan drippings. Cook until softened, 1 to 2 minutes. Add marsala and bring to a boil, scraping up browned bits from bottom of pan. Boil, stirring often, until slightly reduced, about 3 minutes. Stir in lemon juice. Season with additional salt and pepper to taste. Return chicken and any juices that have accumulated on plate to sauce to heat. Serve chicken and sauce garnished with parsley.