Prepare the lemon, parsley, and garlic so they’re ready to go when you need them. Roughly chop the parsley leaves, juice the lemon, and mince the garlic. Set these ingredients aside.
Trim the chicken breasts of excess fat. Cover them with plastic wrap and pound them with a mallet or rolling pin until they are an even thickness (about 1/2-3/4 inch thick). Cut each chicken breast in half so that you have four to six pieces about the size of the palm of your hand. Season both sides of the chicken pieces with salt and pepper.
Heat the olive oil in a heavy skillet, over medium heat. While the oil is heating, place the flour in a bowl and lightly coat each piece of chicken on both sides. When the oil is very hot but not smoking, add the chicken pieces to the skillet and cook until golden brown on each side (about 3-5 minutes on each side). Cook the chicken in batches, if needed, to prevent them from overcrowding the skillet. Transfer the browned chicken on a clean plate.
After removing the chicken from the skillet, turn the heat down to medium-low and add the butter and minced garlic. Sauté the garlic in the butter for about one minute. Add the chicken broth and lemon juice to the skillet and whisk to dissolve (or “deglaze”) the brown bits off of the bottom of the pan.
Add the capers and half of the chopped parsley to the skillet. Increase the heat to medium, add the chicken back to the skillet, and spoon the sauce over top. Allow the chicken to simmer in the sauce for 3-5 minutes, without a lid, or until the sauce reduces by half. The flour on the chicken will help thicken the sauce as it simmers. Sprinkle the remaining parsley over top just before serving.
*I use Better Than Bouillon to mix up the exact amount of broth needed, when needed.