Start by pounding the chicken breasts to an even thickness of about 1.5 cm, then season them lightly with salt and pepper. Set up a shallow dish with flour and lightly dredge each piece, shaking off the excess for a thin, even coating.
Heat the olive oil in a large skillet over medium-high heat until shimmering and just starting to smoke. Carefully place the chicken breasts in the pan and cook for about 3-4 minutes on each side, until they are golden brown and cooked through. Remove the chicken from the pan and set aside.
Add the minced garlic to the same pan and cook until fragrant, about 30 seconds, stirring constantly. Pour in the white wine or chicken broth and scrape up any browned bits from the bottom of the pan, letting it simmer for 2 minutes until slightly reduced.
Stir in the lemon juice and lemon zest, then add the rinsed capers. Return the chicken to the pan and spoon the sauce over the top. Cook for another 2-3 minutes, allowing the flavors to meld and the chicken to reheat slightly.
If using, swirl in the butter to the sauce for extra richness and shine. Taste the sauce and adjust with more lemon or salt if needed. Sprinkle with chopped parsley just before serving for a fresh, vibrant finish.
Transfer the chicken to plates, spoon the glossy, tangy sauce over the top, and garnish with additional parsley if desired. Serve immediately with your favorite side for a bright, flavorful meal.