Prepare the chicken: Place the chicken breasts between two sheets of plastic wrap or parchment paper.
Use a meat mallet or rolling pin to pound the chicken to an even thickness of about ½ inch.
Season both sides of the chicken with salt and pepper.
Dredge the chicken: In a shallow dish, pour in the flour.
Coat each chicken breast evenly with flour, shaking off the excess.
Cook the chicken: Heat 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 aside.
Make the sauce: In the same skillet, reduce the heat to medium and add butter.
Once melted, pour in the lemon juice and white wine, scraping the bottom of the pan to release brown bits.
Add the chicken broth and capers, stirring to combine.
Let the sauce simmer for 2-3 minutes until slightly thickened.
Combine the chicken and sauce: Return the chicken to the skillet, ensuring it's coated with the sauce.
Simmer for another 2 minutes, allowing the chicken to absorb some of the sauce.
Serve: Garnish with chopped parsley and serve immediately.