Pat each chicken breast dry with paper towels, then place between two sheets of plastic wrap. Pound them to about 1.5cm (0.6in) thickness using a meat mallet or rolling pin. Season generously with salt and pepper.
Spread the flour on a shallow dish. Dredge each piece of chicken in the flour, shaking off any excess to create a light, even coating.
Heat the olive oil in a large skillet over medium heat until shimmering. Carefully add the chicken breasts and cook for about 3-4 minutes per side, until golden brown and cooked through. Transfer to a plate and set aside.
Add the butter to the same pan, allowing it to melt and foam. Stir in the minced garlic and cook for about 30 seconds until fragrant, making sure not to burn it.
Pour in the white wine, scraping the browned bits from the bottom of the pan with a spatula. Bring to a gentle simmer and cook for 2 minutes, reducing slightly.
Stir in the lemon juice and rinsed capers. Let the sauce simmer for about 1 minute to meld the flavors and slightly thicken. If needed, stir in a small cornstarch slurry to achieve a glossy finish.
Return the cooked chicken to the pan, spooning the sauce over each piece. Cook for another minute until heated through and coated with the sauce.
Transfer the chicken to serving plates, spooning extra sauce over the top. Garnish with chopped parsley for a fresh, vibrant finish.
