Season the chicken breasts with salt and pepper, then dredge them in flour, shaking off the excess.
In a large skillet, heat the olive oil and 2 tablespoons of butter over medium-high heat.
Add the chicken breasts to the skillet and cook for about 3-4 minutes on each side until golden brown and cooked through. Remove the chicken and set aside.
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 pan.
Return the chicken to the skillet and cook for an additional 2 minutes, allowing the flavors to meld.
Remove the chicken again and stir in the remaining butter until melted and the sauce is slightly thickened.
Serve the chicken topped with the sauce and garnish with fresh parsley.
Notes
For a gluten-free version, substitute all-purpose flour with a gluten-free flour blend.
Serve with pasta or rice to soak up the delicious sauce.
Adjust the amount of lemon juice according to your taste preference.