Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; with a meat hammer, pound the chicken to 1/2-inch thickness. Place 1 teaspoon of flour in a small bowl, and place remaining flour in a shallow dish. Sprinkle salt and pepper evenly over both sides of the chicken. Dredge the chicken in flour in a shallow dish and shake off the excess.

Melt 1 tablespoon of butter in a large skillet on medium-high heat. Add 1 tablespoon oil to pan and swirl it around to coat. Add the chicken to pan and sauté for 4 minutes on each side or whenever it's done. Remove chicken from pan and keep it warm.

Heat the remaining tablespoon of oil in the pan and coat it with a swirl. Add shallots to the pan and sauté and stir frequently for 3 minutes. Add garlic and continue to sauté for 1 minute, stirring constantly. Add wine and bring to a boil, scraping the pan to loosen any browned bits that clump up. Cook everything until the liquid has almost evaporated, stirring occasionally. Add 1/4 cup broth to reserved 1 teaspoon flour and stir until it becomes smooth. Add the remaining 1/2 cup broth to pan and bring it to a boil. Cook for about five minutes until it's reduced by half. Stir in the flour mixture, then cook for 1 minute or until slightly thick, while continuing to frequently stir. Remove it from the heat and; stir in the remaining 1 1/2 tablespoons butter, juice, and capers (lot of stirring, huh?). Place 1 chicken breast half on each of the 4 plates and top each with about 2 tablespoons sauce. Sprinkle each serving with about 2 teaspoons parsley and you're done.