Place each breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or small heavy skillet. Place flour in a shallow dish, and dredge chicken in flour.
Heat butter and oil in a large skillet over medium-high heat. Add chicken, and cook for 3 minutes on each side or until browned. Remove chicken from pan; keep warm. Add white wine, 1/4 cup lemon juice, capers, and garlic to pan; scrape pan to loosen browned bits. Cook for 2 minutes or until slightly thick. Sprinkle with salt and pepper. Serve chicken over pasta. Top with sauce; sprinkle with parsley.
Wine note: When a recipe calls for wine as an ingredient, it's nice to find a bottle that is delicious enough to drink but affordable enough to toss a little in the skillet. Mani Masianco 2005 ($15), an Italian blend of pinot grigio and verduzzo, fills the bill. It's aromatic, with apple, lemon, and floral notes. It also has the necessary acidity to greet the potent acid of the capers. -Jeffery Lindenmuth