Place chicken breasts between two sheets of plastic wrap and pound them to an even thickness.
Dredge the chicken cutlets in flour and shake off the excess.
In a large skillet over medium-high heat, heat olive oil. Sauté the chicken for 3-4 minutes per side until golden brown and cooked through. Remove and set aside.
In the same skillet, add lemon juice, chicken broth, and capers, scraping any browned bits off the bottom. Bring to a boil, then reduce heat and simmer for 5 minutes.
Remove the skillet from heat and stir in cold butter until melted and the sauce is smooth.
Return the chicken to the skillet, spooning sauce over the top. Sprinkle with fresh parsley before serving.