1. Season chicken breasts with salt and pepper. Dredge in flour, shaking off excess.
2. 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.
3. In the same skillet, add lemon juice, chicken broth, and capers. Bring to a boil, scraping up brown bits from the pan.
4. Return chicken to the skillet and simmer for 5 minutes. Remove chicken and place on a serving platter.
5. Add remaining butter to the skillet and whisk until sauce thickens. Pour sauce over chicken and serve.