Old Market Building, also known as the Rice Museum, is a historic public market building located at Georgetown, Georgetown County, South Carolina. It was built in 1832–1835, and is a one-story, Classical Revival temple-form building on a high arcaded base.

The arched area was used as an open-air market but was enclosed in the early-20th century. A tower topped by a square stage and an open belfry was added. The tower houses a four-sided clock that was added in about 1842. The building has served as a town hall, a jail, an open-air market, and a slave market.

It was listed on the National Register of Historic Places in 1969.