Stock Photo: Postcard of Conway Building in Chicago. ca. 1914, 357. THE CONWAY BUILDING, CHICAGO. The Conway Building, located on the southwest corner of Clark and Washington Sts., is a massive office building, 21 stories high. It is a steel structure resting on concrete caissons which are sunk 100 feet to bedrock, the outside facing being granite terra cotta and enameled brick. Sixteen electric passenger elevators of the latest type provide fast and efficient service to the upper floors.