Season the chicken breasts with salt and pepper on both sides.
Dredge the chicken in flour, shaking off excess.
In a large skillet, melt 2 tablespoons of butter and 2 tablespoons of olive oil over medium heat.
Add the chicken breasts and cook for 3-4 minutes on each side until golden brown.
Remove the chicken from the skillet and set aside.
In the same skillet, add chicken broth, scraping up browned bits from the bottom.
Stir in the lemon juice and capers, simmering for 2 minutes.
Return the chicken to the skillet, cooking for an additional 2-3 minutes.
Remove the chicken again and whisk in the remaining butter until melted.
Serve the chicken topped with the sauce and garnish with fresh parsley.