Cut each chicken breast horizontally in half to produce two thin slices. Put the flour on a large plate and season with salt and pepper.
Dip the chicken in the flour to lightly coat, then shake off any excess flour.
Heat the oil and half the butter in a large frying pan over a medium heat. Once the butter has melted add the chicken and fry for 5-6 minutes on each side or until golden brown and cooked through.
Transfer to a warmed dish using a slotted spoon, then cover with foil to keep warm.
Add the lemon juice, stock and capers to the pan juices. Stir and scrape the bottom of the pan to release any sticky bits. Bring to the boil, stirring, and boil for one minute.
Add the parsley and the remaining butter and simmer for a further minute, stirring until blended.
Serve immediately with the sauce drizzled over the chicken.