Slice chicken breasts lengthwise and pound to ½-inch thickness. Season both sides with salt and pepper.
Dredge chicken lightly in flour, shaking off excess.
Heat 2 tablespoons olive oil and 1½ tablespoons butter in a large skillet over medium-high heat until hot.
Cook half the chicken until golden and released easily, about 2½–3 minutes per side. Remove and repeat with remaining chicken using the last tablespoon of oil.
Reduce heat to medium. Add remaining butter to skillet, then pour in wine and capers. Scrape up browned bits and simmer 2 minutes.
Add chicken stock, lemon juice, and lemon zest. Simmer another 2 minutes.
Return chicken to skillet and simmer gently, turning occasionally, until cooked through and sauce thickens slightly, 3–5 minutes.
Remove from heat and sprinkle with parsley. Serve immediately.