Season the chicken breasts with salt and pepper.
Dredge the chicken in flour, shaking off any excess.
In a large skillet, melt 2 tablespoons of butter with 1 tablespoon of olive oil over medium-high heat.
Add the chicken in batches and cook until golden brown on each side, about 3 minutes per side.
Remove the chicken from the skillet and set aside.
In the same skillet, add the chicken broth, white wine, and lemon juice. Bring to a boil while scraping up any browned bits from the bottom of the pan.
Let the sauce simmer until it is reduced by half, about 5 minutes.
Stir in the remaining 2 tablespoons of butter until melted.
Return the chicken to the skillet and add the capers. Cook for an additional 2 minutes.
Garnish with fresh parsley before serving.
