Heat butter and oil in a skillet over medium-high heat. Cook chicken in batches, flipping once, until golden and cooked through - about 3-4 minutes per side.
Thicken sauce: Cook wine until almost evaporated (3-5 mins), stir in capers on low heat. Finish: Add remaining butter, let melt and stir in. Adjust seasoning: Taste test, add salt/pepper if needed.