Mix flour, salt, and pepper in a shallow dish. Dredge each chicken breast in the flour mixture, shaking off excess.
Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat. Cook chicken for 4-5 minutes per side until golden brown and cooked through. Transfer to a plate.
Add chicken broth and lemon juice to the skillet, scraping up any browned bits from the bottom. Bring to a boil and let simmer for 3-4 minutes until reduced by half.
Stir in capers and remaining 2 tablespoons butter, swirling the pan until the butter melts and the sauce is glossy.
Return chicken to the skillet, spoon sauce over the top, and simmer for 1-2 minutes. Garnish with fresh parsley before serving.