Season chicken cutlets evenly with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add chicken and cook for 3–4 minutes per side until golden and cooked through. Remove chicken from the skillet and set aside.
Pour chicken broth into the skillet and scrape up any browned bits.
Add lemon juice and capers, then simmer for 2–3 minutes until slightly reduced.
Stir in butter until melted and the sauce is glossy.
Return chicken to the skillet and spoon sauce over the top.
Cook for 1–2 minutes to warm through.
Sprinkle with fresh parsley and serve immediately.