Start by preparing the chicken breasts. Place each breast between two sheets of plastic wrap or parchment paper and gently pound them to an even thickness of about 1/2 inch. Season both sides with salt and pepper.

Dredge the chicken breasts in flour, making sure to coat them evenly. Shake off any excess flour.

Heat the olive oil in a large skillet over medium-high heat. Once hot, add the chicken breasts and cook for 3-4 minutes on each side, until golden brown and cooked through. Remove the chicken from the skillet and set it aside on a plate.

In the same skillet, melt the butter. Add the lemon juice and chicken broth, scraping up any browned bits from the bottom of the pan with a wooden spoon. Stir in the capers.

Bring the sauce to a simmer and cook for 2-3 minutes until the sauce thickens slightly. Taste and adjust the seasoning if necessary.

Return the chicken to the skillet, spooning the sauce over the top. Cook for another 1-2 minutes to heat the chicken through and allow the flavors to meld.

Transfer the chicken to serving plates, drizzle with the sauce, and garnish with fresh parsley. Serve immediately.