Begin by placing the chicken breasts between two sheets of plastic wrap or parchment paper. Use a meat mallet or rolling pin to pound them to an even thickness of about 1/2 inch. Season both sides with salt and pepper.
Dredge each chicken breast in 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.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
Pour in the chicken broth and lemon juice, scraping the bottom of the skillet to deglaze. Bring the mixture to a simmer.
Stir in the capers and return the chicken to the skillet. Cook for an additional 2-3 minutes, allowing the chicken to absorb the flavors.
Remove the skillet from heat and stir in the remaining 2 tablespoons of butter until melted.
Serve the chicken hot, garnished with chopped parsley and lemon slices.