Sometimes a chimney may have reached the point where rebuilding is not possible.  In this case, either a masonry chimney or a wood chase chimney can be built.  The wood chase would have the correctly rated flue pipe inside, and would be either sided with vinyl siding, or have cultured stone covering.  Also, Building Codes for safety require that chimney top be minimum of 2 feet higher than any point of roof within 10 feet, so sometimes chimney extension may be advised to meet current Building Codes.