Preheat oven to 350 degrees. Gently pull chicken skin away from flesh without removing; leave skin attached at several points. Combine melted butter, garlic, thyme and parsley in a small bowl. Using a pastry brush, paint the butter mixture all over chicken and under the skin.
Arrange potato slices, overlapping slightly, in a lightly greased 13x9x2 inch baking dish. Season with salt and pepper. Arrange onion slices on top. Place chicken pieces skin side up on top of potato-onion slices. Brush again with garlic butter. Bake for 1 hour, basting every 20 minutes with remaining garlic butter.