Prepare the chicken: In a shallow dish, combine flour, salt, and pepper. Dredge chicken breasts in the flour mixture, shaking off any excess.
Cook the chicken: Heat butter and olive oil in a large skillet over medium-high heat. Add chicken breasts and cook for 3-4 minutes per side, or until golden brown and cooked through. Remove chicken from skillet and set aside.
Make the sauce: In the same skillet, add lemon juice, chicken broth, and capers. Bring to a simmer and cook for 1-2 minutes, or until slightly thickened.
Finish and serve: Return chicken breasts to the skillet and coat with the sauce. Sprinkle with chopped parsley and grated Parmesan cheese. Serve immediately with pasta, rice, or vegetables.