Split chicken breast halves in half horizontally to form 4 cutlets. If using 4 ounce breasts, do not split but continue with recipe. Place each cutlet between 2 sheets of heavy-duty plastic wrap; pound each cutlet to 1/4-inch thickness using a meat mallet or small heavy skillet. Sprinkle cutlets evenly with salt and pepper. Place flour in a shallow dish; dredge cutlets in flour.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Add 2 cutlets to pan, and sauté 2 minutes. Turn cutlets over; sauté for 1 minute. Remove the cutlets from pan. Repeat the procedure with remaining 1 tablespoon butter and 2 cutlets.
Add wine to pan and bring to a boil, scraping pan to loosen browned bits. Cook for 1 minute or until liquid almost evaporates. Stir in chicken broth; bring to a boil. Cook until broth mixture is reduced to 2 tablespoons (about 4 minutes). Stir in juice and capers. Serve over chicken. Sprinkle with parsley.