I discovered from an article in today's The Hindu that Chennai has more museums than any other city in India. Unfortunately, the exhibits are poorly displayed and not very informative. This is The Government Museum at Egmore, inaugurated in 1851. According to the Hindu article, the museum is internationally known mainly for its Amaravati sculptures, bronzes, coins and medals. It has the largest collection of Roman coins outside Europe. (The reason is Indo-Roman trade. There's an article about that here.)
This building is a fine example of the Indo-Saracenic style of architecture, a British Imperial hybrid. Call it Orientalist, but I like it.