Place chicken breasts on a cutting board and with a sharp knife slice them in half horizontally. Then cover them with a piece of plastic wrap or parchment paper and pound with a meat mallet or a rolling pin until they are no more than ½ inch thick throughout. Then remove the plastic wrap and season them with salt and pepper on both sides.
Juice half an orange and slice the other half. Peel and chop the shallots and slice the garlic cloves. In a frying pan heat 1 tablespoon of olive oil and brown the chicken cutlets for 2-3 minutes on each side. Remove to a plate and set aside.
Add 1 tbsp of butter to the pan and saute the shallots and sliced garlic for 3 minutes over low heat, then add the dry sherry and let it simmer for a couple of minutes until slightly reduced. Then add the orange juice, the remaining butter and capers, bring to a boil, then lower the heat and return the chicken to the pan. Baste the chicken with the sauce and top with orange slices. Taste the sauce and adjust the seasoning if needed and let the chicken warm through in the pan for a few minutes, then sprinkle with chopped parsley and serve.