Pound chicken breasts to ½-inch thickness and season with salt and pepper.
Place flour in shallow dish for dredging.
Heat 2 tablespoons butter and 2 tablespoons olive oil in large skillet over medium-high heat.
Dredge chicken in flour and cook 3-4 minutes per side until golden brown; transfer to plate.
Add chicken broth to pan and scrape up browned bits.
Add lemon juice and let reduce for 3 minutes.
Stir in capers and remaining 2 tablespoons butter.
Return chicken to pan, simmer 2-3 minutes.
Garnish with fresh parsley and serve immediately.