Quincy Market is a historic building near Faneuil Hall in downtown Boston, Massachusetts. It was constructed between 1824 and 1826 and named in honor of mayor Josiah Quincy, who organized its construction without any tax or debt. The market is a designated National Historic Landmark and a designated Boston Landmark in 1996, significant as one of the larges…Quincy Market is a historic building near Faneuil Hall in downtown Boston, Massachusetts. It was constructed between 1824 and 1826 and named in honor of mayor Josiah Quincy, who organized its construction without any tax or debt. The market is a designated National Historic Landmark and a designated Boston Landmark in 1996, significant as one of the largest market complexes built in the United States in the first half of the 19th century. According to the National Park Service, some of Boston's early slave auctions took place near what is now Quincy Market.