Season chicken with salt and pepper.
Dredge chicken in flour and shake off excess.
In a large skillet over medium heat, melt 2 tablespoons of butter with 3 tablespoons olive oil. When butter and oil start to sizzle, add chicken and cook for 3 minutes. When chicken is browned, flip and cook other side for 3 minutes.
Remove pan from heat and remove chicken to a plate.
Into the pan add the lemon juice, stock and capers.
Return to stove and bring to boil, scraping up brown bits from the pan for extra flavor. Check for seasoning. Return the chicken to the pan and simmer for about 5 minutes. Remove chicken to platter. Add remaining 2 tablespoons butter to sauce and whisk vigorously. Pour sauce over chicken and garnish with parsley.