It's housed in an ostentatiously ornate palace, commissioned in 1891 by the Rothschild family, whose fortune was boosted by the city's first oil boom, as was that of the Nobel family.
More than a century on, its legacy — wide squares and elegant boulevards lined with belle-époque mansions — is lovelier than the forests of derricks and glimpses of silvery pipeline that define the industry now.
Head out of town to Baku's most famous monument, the Temple of Ateshgah, a Zoroastrian, then Hindu religious site, where oil used to spring from the ground and ignite spontaneously. You're as likely to be struck by its desolate industrial setting and the acrid odour of oil as the sacred architecture and symbolism.
But then Baku isn't an obvious tourist destination. Yet, next year, Four Seasons opens a palatial hotel on the waterfront, as will Hilton and Marriott, which is also developing a beach resort (in the meantime there's a Park Hyatt and a couple of adequate boutiques in the Old City). So it's bound to change.
For the moment, though, it's a chance to experience a megalopolis in the making: somewhere roaring, rich and infectiously optimistic but somehow not quite worldly and not quite there, which gives it genuine intrigue and charm.
DETAILS
THE FLIGHT BMI flies to Baku, returns from Heathrow from £792, www.flybmi.com.
THE HOTELS Park Hyatt, doubles from £255, www.parkhyattbaku.com Sultan Inn, doubles from £272, www.sultaninn.com Museum Inn, doubles from £214, www.museum-inn.az
THE CLUBS Baku Jazz Center, 19 Rashid Behbudov, jazzcenter.jazz.az Chinar, 1 Shovket Alekperova Street, www.chinar-dining.az Opera Lounge, 9 Izmir Street, www.operalounge.az