Put a skillet on at medium high. Add just enough olive oil to cover the bottom and half of the butter.Salt and pepper one side of the chicken fillets and lay the fillets in the skillet with the seasoned side down. Salt and pepper the up side. Cook them about 3-5 minutes a side until the juices run clear and/or they read 165F on a meat thermometer.
Remove them to a dish that will catch the drippings.Add the rest of the butter. Squeeze in the lemon juice and add the lemon rind and the parsley.
Reduce the heat to medium and stir it all together. Put the fillets and the drippings back into the skillet. Turn them over a few times and spoon the liquids on them a few times as they warm back up.
Then serve up your Easy Chicken Fillet Recipe with Parsley, Lemon and Butter. With the liquids from the skillet spooned on top.