Season both sides of the chicken breasts with salt and pepper. Dredge each chicken breast in the flour, shaking off the excess.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 4-5 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set it aside on a plate.
In the same skillet, melt the butter over medium heat. Add the chicken broth, lemon slices, and capers. Stir, scraping up any brown bits from the bottom of the pan for extra flavor. Add the white wine (if using) and bring the mixture to a simmer. Let the sauce cook for 3-4 minutes until it reduces slightly.
Return the chicken to the skillet, spooning some of the sauce over the top. Let the chicken simmer in the sauce for another 2-3 minutes until heated through. Sprinkle with fresh parsley before serving.