Butterfly your chicken breast and cut in half, length wise. Pound the chicken out so that they're all flat and even.
Salt and pepper each side and dredge in flour, shaking off the excess.
In a large skillet over medium high heat, melt 2 tablespoons of butter with 3 tablespoons olive oil. When butter and oil start to sizzle, add 2 pieces of chicken and cook for 3 minutes. Flip and cook other side for 3 minutes. Remove and transfer to plate. Melt 2 more tablespoons butter and add another 2 tablespoons olive oil. When butter and oil start to sizzle, add the other 2 pieces of chicken and brown both sides in same manner. Remove pan from heat and add chicken to the plate. Cover with foil to keep warm.
Add the lemon juice, broth and capers. Return to stove and bring to boil, scraping up brown bits from the pan for extra flavor. Return all the chicken to the pan and simmer for 5 minutes. Remove chicken onto a serving plate.
Add remaining 2 tablespoons butter to sauce and whisk vigorously. Pour the sauce over chicken and garnish with parsley. Serve right away & enjoy!