The first Fannie May retail store was opened by H. Teller Archibald in 1920 at 11 N. LaSalle St. in Chicago. By 1935 there were nearly four dozen retail stores in Illinois and several neighboring states.The first Fannie May retail store was opened by H. Teller Archibald in 1920 at 11 N. LaSalle St. in Chicago. By 1935 there were nearly four dozen retail stores in Illinois and several neighboring states.