Slice each chicken breast in half lengthwise to make four thin pieces.
Sprinkle both sides with salt and pepper.
Place the flour on a plate and coat each piece of chicken lightly. Shake off extra flour.
Heat olive oil and 1 tablespoon butter in a large skillet over medium heat.
Cook the chicken for 3–4 minutes per side until golden and cooked through. Remove it to a plate.
Pour chicken broth and lemon juice into the pan. Scrape the bottom with a spoon.
Stir in capers and the last tablespoon of butter. Let the sauce simmer for 2–3 minutes.
Return the chicken to the pan and spoon sauce over the top. Sprinkle with parsley.