Slice chicken breast in half lengthwise (like you are butterflying it) making 2 equal pieces. Place the chicken between wax paper and pound until they are somewhat even.
Season the chicken with salt and pepper and add about 1/4 – 1/2 cup of flour to a large Ziploc bag. Dredge chicken in flour and shake off excess.
In a large skillet over medium high heat, add 3 tablespoons olive oil. When the oil is warm add 3 Tbsp of butter. After the butter melts and starts to sizzle, add 2 pieces of chicken and cook for 4 minutes. When chicken is browned, flip and cook other side for 3 minutes or until no longer pink.
Transfer the chicken to a plate to keep it warm and repeat with remaining chicken, adding more oil/butter as needed.
Into the pan add the lemon juice, stock and capers. Bring to boil, scraping up brown bits from the pan for extra flavor and reduce by half. Check for seasoning. Add the remaining 2 Tbsp of butter and parsley.
Place the chicken on a platter and pour sauce over.