Slice chicken breasts in half lengthwise and place each piece between two pieces of plastic wrap or wax paper. Pound out to an even thickness of about ½-inch. Season with salt and pepper.
Add flour to a shallow dish and season with salt and pepper. Stir to combine.
Working one at a time, dredge chicken in flour, pressing flour into chicken. Gently shake off excess and set aside.
In a large skillet over medium-high heat, heat 2 tablespoons of the olive oil. Working in batches if needed, brown cutlets on one side until deep golden brown, about 2 minutes, without disturbing them.
Flip and cook until the chicken is nearly cooked through, about 30 seconds. Remove to a plate and set aside.
Add garlic and remaining olive oil to skillet. Cook, stirring frequently, until garlic is golden brown, about 2 minutes.
Add wine and capers and cook, scraping up any brown bits from pan, until liquid is almost gone, about 3 minutes.
Add ½ cup of water, then the butter. Swirl pan while butter melts, about 1 minute.
Return chicken to skillet and let cook until chicken is cooked through and sauce has thickened, about 2 minutes.
Remove from heat and stir in lemon juice. Adjust seasoning as needed.
Serve and enjoy!
