High Quality Content by WIKIPEDIA articles! The Alexandria City Hall also known as the Alexandria Market House & City Hall, in Alexandria, Virginia, is a building built in 1871 and designed by Adolph Cluss. It was listed on the U.S. National Register of Historic Places in 1984. The site was originally a market from 1749 and courthouse from 1752. A new building was constructed in 1817 but after an extensive fire in 1871 it was rebuilt as a replica of the former building.