Pound the chicken breasts with a meat tenderiser, or use chicken cutlets.
Season the chicken generously with salt and pepper. Dredge them in flour and shake off excess.
In a large skillet melt half of the butter with the extra-virgin olive oil, over medium heat.
Add the chicken slices to the skillet and cook for about 3 to 4 minute per side until golden. Remove the chicken from the skillet and set aside in a warm place.
Adjust the heat to very low. Add lemon juice, chicken stock or wine, capers, lemon slices and shallots, and scrape well up the brown bits from the pan.
Return the skillet to medium heat and bring to a boil. Season to taste, add the chicken back to the skillet and simmer for about 5 minutes.
Remove the chicken and place into a serving plate. Add the remaining butter to the sauce and whisk for about a minute until it has a nice, silky texture.
Pour the sauce over the chicken and garnish with parsley or fresh thyme leaves. Season with freshly-cracked black pepper and serve.