Sprinkle the chicken with the salt and pepper. Dredge the chicken in the flour to coat lightly. In a large sauté pan, melt 2 tablespoons of butter with 2 tablespoons of oil over medium-high heat. Add the chicken and cook just until brown, about 3 minutes per side. Using tongs, transfer the chicken to a plate.

Add the broth, lemon juice and capers to the same pan. Bring the broth mixture to boil over medium-high heat, scraping up the brown bits from the bottom of the pan for extra flavor. Return the chicken to the pan and simmer until just cooked through, about 5 minutes. Using tongs, transfer the chicken to a platter. Whisk the remaining 2 tablespoons of butter into the sauce. Pour the sauce over the chicken, garnish with the parsley, and serve.