Slice chicken breasts to half its thickness and pound chicken to 1/4". Season chicken with salt and pepper. Dredge chicken in flour and shake of excess.
In a large skillet over medium high heat, melt 3 tablespoons butter with 3 tablespoons olive oil. When butter and oil start to sizzle, add chicken and cook for 3 minutes per side Remove chicken and transfer to a plate for a few minutes.
Into the pan add the lemon juice, chicken stock and capers. Return to the stove and bring to a boil, scraping up brown bits from the pan for extra flavor. Check for seasoning. Return chicken to the pan and simmer until chicken is completely cooked.
Remove chicken to platter when cooked and add remaining butter to sauce and whisk vigorously. Add flour to thicken, if necessary. Pour sauce from pan over chicken and garnish with parsley, if desired.
NOTE: You may need to add more butter and oil for browning chicken depending on how much chicken you cook. Also, capers are a big key in this recipe. They can be found usually by the black and green olives at the grocery store. They are from the olive family!