Pat chicken dry with paper towels and pound thin. I use cutlets and put them in a plastic bag to pound them flat. Season with salt and pepper. Dredge each cutlet in flour and shake lightly to remove excess.
In a large skillet over medium-high heat, melt butter (and olive oil, if desired) until shimmering. Add chicken and cook until golden brown on both sides, about 5 minutes, flipping halfway through. Transfer chicken to a plate and tent with foil.
Add wine and lemon juice to skillet, scraping up any brown bits from the bottom. Remove from heat and stir in cold butter until incorporated. Stir in capers.
Pour sauce over chicken and serve.