Fireplace and Chimney Construction - Masonry These are generally constructed of brick or stone. The firebox may be metal but is most often built of firebrick. The chimney is usually lined with a terra cotta liner. Masonry is strong and durable and adds an air of structural soundness to the house. Brick and stone impart feelings of permanence and stability while adding a quiet beauty both inside and out. These range in price from $2,000 and up.