Sprinkle the chicken cutlets with salt and pepper. Set aside.Heat the butter in a medium skillet over medium-high heat. Lightly brown the chicken on both sides and then transfer to a plate.Add the garlic to the pan and saute for a minute. Add the chicken broth and white wine and bring to a boil until reduced by half, about 3-5 minutes. Add the parsley, lemon juice and salt.Arrange the chicken pieces in the skillet and top with the lemon slices, olives and capers. Bring to a simmer over medium heat, cover and simmer for about 15 minutes. Add salt to taste. If the sauce is too thin, dissolve a little cornstarch in a little water and stir it into the sauce, simmering it for another minute.
Serve the chicken topped with the lemons, olives and capers, spoon some sauce over, and sprinkle with the fresh parsley. Serve with steamed rice or pasta.