Prepare the Chicken: Place the chicken breasts between two pieces of plastic wrap and pound them to an even thickness of about 1/2 inch. This helps them cook evenly.
Season the Flour: In a shallow plate, combine the flour, salt, black pepper, and garlic powder. Dredge each chicken breast in the flour mixture, shaking off the excess.
Sear the Chicken: In a large skillet, heat the olive oil and 1 tablespoon of butter over medium-high heat. Once the pan is hot, add the chicken breasts and cook for about 4-5 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.
Make the Sauce: 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 skillet. Allow the sauce to cook for about 3-4 minutes to reduce slightly.
Finish the Dish: Return the chicken to the skillet and let it simmer in the sauce for an additional 2 minutes. Add the remaining tablespoon of butter and swirl it into the sauce until melted and combined.
Serve: Plate the chicken and spoon the sauce over the top. Garnish with chopped fresh parsley and lemon slices.