Use a sharp knife to cut each chicken breast in half horizontally. Transfer the chicken to a foil-lined grill pan and season.
Put the oil, butter, lemon juice, parsley and oregano in a small pan and heat until the butter is melted. Spoon or brush this mix over the chicken.
Grill the chicken in batches under a preheated hot grill for about 4 minutes until just cooked and still succulent. Serve immediately with lemon wedges and, if liked, wholewheat pasta.