Slice the chicken breasts horizontally and pound them thin until evenly flattened.
Season both sides of the chicken with salt and pepper. Lightly dredge each piece in flour, shaking off any excess.
Heat olive oil in a large skillet over medium-high heat. Sear the chicken for about 3–4 minutes per side until golden brown. Work in batches if necessary so the pan does not become overcrowded.
Remove the chicken from the skillet and set aside on a plate.
Deglaze the pan with the white wine, scraping up any browned bits from the bottom of the pan.
Add the chicken broth, lemon juice, and capers. Bring the sauce to a simmer and allow it to reduce slightly for about 3–4 minutes.
Return the chicken to the skillet and spoon the sauce over the top. Let the chicken simmer in the sauce for another 2–3 minutes.
Remove the pan from the heat and whisk in the butter until the sauce becomes smooth and glossy.
Finish with chopped parsley and garnish with lemon slices if desired. Serve immediately.