Season chicken with salt and pepper. Dredge chicken in flour and shake off excess.
In a large frying-pan over medium high heat, melt two tablespoons of butter with three tablespoons olive oil. When butter and oil start to sizzle, add two pieces of chicken and cook for three minutes. When chicken is browned, flip and cook other side for three minutes. Remove and transfer to plate. Melt two more tablespoons of butter and add another two tablespoons of olive oil. When butter and oil start to sizzle, add the other two pieces of chicken and brown both sides in same manner. Remove pan from heat and add chicken to the plate.
Into the pan add the lemon juice, stock and capers. Return to hob and bring to boil, scraping up brown bits from the pan for extra flavor. Check for seasoning. Return all the chicken to the pan and simmer for five minutes. Remove chicken to platter. Add remaining two tablespoons butter to sauce and whisk vigorously. Pour sauce over chicken and garnish with parsley.