Prepare the Chicken: Start by slicing each chicken breast lengthwise to create thinner pieces. Sprinkle salt and pepper evenly on both sides. Place the flour in a shallow dish and lightly coat each piece, shaking off extra flour.
Heat the Pan: Set a large skillet over medium heat. Add olive oil and one tablespoon butter. Let the fat warm until it looks glossy and ready for cooking.
Cook the Chicken: Lay the chicken pieces into the pan in a single layer. Cook until golden on the first side, then flip and cook the other side until fully done. Transfer chicken to a plate and keep it warm.
Build the Sauce: Lower the heat slightly. Pour white wine into the pan and scrape up any browned bits. Let the liquid simmer until slightly reduced. Add lemon juice, capers, and remaining butter. Stir gently until the sauce turns smooth and shiny.
Bring It Together: Return the chicken to the pan. Spoon sauce over each piece and let everything simmer briefly so the flavors blend nicely.
Finish and Serve: Sprinkle chopped parsley over the top and serve right away with plenty of sauce.
