If your chicken breasts have tenderloins attached, remove and reserve them for another use. Place the chicken breasts between 2 sheets of plastic wrap and pound gently to an even thickness of 1/2 inch, then slice them on the bias into 1/2-inch wide strips.
Combine the flour, 3/4 teaspoon of salt and a few grinds of black pepper in a 1-quart food storage bag and add the chicken strips. Shake the bag to coat the chicken with the flour mixture and set aside.
Cook and drain the pasta according to package directions. Return it to the pan and drizzle with 1 to 2 tablespoons of olive oil. Toss and set aside.
Add another tablespoon or two of olive oil to a large frying pan and place over medium-high heat. Add the butter and as soon as it begins to foam, add the chicken a few pieces at a time, shaking off the excess flour as you do.
Sauté the chicken for 1-1/2 minutes, or until it's barely golden on the outside. It will not be cooked through at this point. Transfer to a plate and set aside.
Add the onion to the pan, reduce the heat to medium and sauté until soft and translucent, 3 to 4 minutes. Add the garlic and continue cooking until fragrant, 1 to 2 minutes longer (do not brown).
Add the chicken broth and bring the mixture to a simmer. Return the chicken to the pan and cook, stirring often, until the broth has thickened slightly, 1-1/2 to 2 minutes.
Add the tomatoes and continue cooking until softened, 2 minutes longer. Season to taste with salt and pepper, then stir in the lemon juice, lemon zest, and parsley. Cook 1 minute longer, then add the chicken mixture to the spaghetti and toss to combine.
To serve, plate individual portions and top with grated Parmesan and a bit of freshly ground black pepper.
Tips for Making This Recipe
The key to success with this recipe is to work quickly and avoid overcooking the chicken while making the pan sauce. Here are some tips for success:
Pound the chicken carefully: When pounding boneless chicken you want to be sure to use the flat side of your mallet and a lighter touch than you would with beef or pork to avoid shredding the meat.
Prep all the ingredients in advance: Chop the onion, mince the garlic, halve the tomatoes, juice and zest the lemon, and chop the parsley before you begin cooking the chicken.
Be careful not to overcook the chicken: In this recipe, the chicken is cooked in two separate steps in order to keep it moist and tender. The first step is to sauté it in a combination of butter and olive oil just long enough for the flour coating to develop a little bit of color. It's important to remember that the chicken will not be fully cooked at this point. It finishes cooking when you return it to the pan to simmer for a couple of minutes in the chicken broth and lemon juice that make up the sauce. Total cooking time for the chicken should only be about 5 minutes.
Add the lemon juice and zest at the end of cooking: In order to keep the citrus flavor in this dish fresh and bright, leave the addition of the lemon juice, lemon zest, and parsley to the last minutes of cooking.