Prepare chicken: Butterfly and pound chicken breasts about ¼ inch thick. Season with salt and pepper.
Dredge: Lightly coat chicken pieces with flour, shaking off excess.
Sear: Heat olive oil and butter in a skillet over medium-high heat. Cook chicken 3 minutes per side or until golden brown. Remove and set aside.
Make sauce: Add garlic to the pan; sauté 30 seconds. Pour lemon juice, zest, white wine (or broth), and capers. Bring to boil, scraping pan for flavor bits.
Simmer: Return chicken to pan. Reduce heat and simmer 4-5 minutes, spooning sauce over chicken.
Finish: Sprinkle fresh parsley on top and serve immediately with sauce.