Mix butter, lime juice, salt and pepper in a medium bowl bowl. Toss chicken in the mixture, cover with plastic wrap and marinate for half an hour in the fridge.
Pre-heat oven to 350F. Place the chicken fillets in a baking dish or pan in one layer and bake for 20 minutes. Turn off the oven and cover the baking dish with a sheet of aluminum foil. Close the oven and continue to bake with the residual heat for another 10 minutes before serving.