Begin by placing the chicken breasts between two pieces of plastic wrap or parchment paper. Use a meat mallet or rolling pin to pound the chicken to an even thickness of about 1/2 inch. Season both sides with salt and black pepper.

Spread the flour on a plate and dredge each chicken breast in the flour, shaking off any excess.

In a large skillet, heat the olive oil and 1 tablespoon of butter over medium-high heat. Once hot, add the chicken breasts and cook for about 4-5 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.

In the same skillet, add the chicken broth, lemon juice, and capers. Bring to a simmer, scraping up any browned bits from the bottom of the pan. Let it cook for about 2-3 minutes to reduce slightly.

Return the chicken to the skillet and cook for an additional 2 minutes, spooning the sauce over the chicken. Remove the skillet from heat and stir in the remaining 2 tablespoons of butter until melted and the sauce is glossy.

Serve the chicken hot, garnished with chopped parsley and lemon slices. Drizzle the sauce over the top.