Fill a large stockpot with water, salt it, and bring to a boil.
Preheat a large skillet with 2 tablespoons of olive oil.
Flatten the chicken in a large Ziploc bag to about ¼ inch thick.
Place the flour in a shallow bowl and season with salt and pepper.
Coat the chicken in the seasoned flour, and add carefully to the skillet. Cook about 3-5 minutes per side until lightly browned. Remove the chicken from the pan.
When the water boils, add the pasta and cook according to the package directions, about 7-9 minutes. When draining the pasta, be sure to reserve some of the hot pasta water.
Make the chicken piccata sauce. Add the butter, lemon juice, wine and pasta water back to the skillet. Cook until the mixture comes to a boil, then add the capers. Pour the sauce into a small bowl or glass measuring cup and set aside.
Make the Pasta al Limone sauce. Add the butter, lemon juice, lemon zest, garlic, wine and pasta water to the skillet. Bring to a boil, then turn off the heat and add the drained pasta. Toss to coat. Add the parsley and parmesan cheese and toss some more. Taste it and add additional salt if needed.
To serve, top the chicken with the reserved Chicken Piccata sauce.