In a shallow bowl, stir together flour, 1/2 teaspoon salt, and 1/4 teaspoon black pepper; set aside. Place a chicken breast half between 2 pieces of plastic wrap. Using the flat side of a meat mallet, lightly pound chicken to about 1/4 inch thick. Remove plastic wrap. Repeat with remaining chicken breast halves. Lightly coat chicken pieces on both sides with flour mixture; shake off excess.
In a small bowl, stir together wine, lemon juice, capers, 1/8 teaspoon salt, and 1/8 teaspoon black pepper. Set aside.
In a very large skillet, melt 2 tablespoons butter over medium-high heat. Add chicken; cook for 5 to 6 minutes, turning to brown evenly. Remove from skillet, reserving drippings in skillet.
Add the remaining 1 tablespoon butter and garlic to skillet drippings. Cook and stir for 1 minute. Stir sauce. Carefully add sauce to the skillet. Cook until sauce is bubbly and reduces slightly (30 to 60 seconds), scraping up the brown bits from the bottom of the skillet. Return chicken to the skillet. Cook for 2 to 3 minutes more or until heated through. Sprinkle with parsley. If you like, garnish with lemon slices. Serve immediately. Makes 4 servings.