Place each chicken breast between two sheets of plastic wrap and gently pound until about ½ inch thick. Season both sides with salt and black pepper.

Dredge each chicken breast in flour, shaking off any excess.

In a large skillet, heat olive oil and 2 tablespoons of butter over medium-high heat. When the oil is hot, add the chicken breasts in a single layer, cooking for about 4-5 minutes on each side until golden brown and cooked through.

Remove the chicken and place it on a plate to rest.

In the same skillet, reduce the heat to medium and add the lemon juice and chicken broth. Stir to deglaze the pan, scraping up any brown bits from the bottom.

Add the capers and bring the sauce to a simmer, cooking for about 2-3 minutes to slightly reduce.

Whisk in the remaining 2 tablespoons of butter until melted and the sauce is smooth. Taste and adjust seasoning with salt and pepper if necessary.

Return the chicken to the skillet, coating each piece in the sauce. Cook for an additional 1-2 minutes to heat through.

Serve the chicken hot, drizzled with the lemon caper sauce, and garnish with chopped parsley if desired.