Season chicken breasts with salt and pepper, then dredge in flour.
Heat olive oil and 1 tablespoon butter in a skillet over medium-high heat. Cook chicken until golden brown, about 3-4 minutes per side. Remove and set aside.
Add lemon juice, chicken broth, and capers to the skillet. Bring to a boil, scraping up brown bits from the pan.
Return chicken to the skillet and simmer for 5 minutes. Remove chicken and add remaining butter to the sauce. Stir until melted.
Serve chicken topped with sauce. Garnish with lemon slices and parsley if desired.