Rotating black holes in a Gödel universe

We construct a five-dimensional, asymptotically Godel, three-charge black hole via dimensional reduction of an asymptotically plane wave, rotating D1-D5-brane solution of type-IIB supergravity. This latter is itself constructed via the solution generating procedure of Garfinkle and Vachaspati, applied to the standard rotating D1-D5-brane solution. Taking all charges to be equal gives a ``BMPV Godel black hole'', which is closely related to that recently found by Herdeiro. We emphasise, however, the importance of our ten-dimensional microscopic description in terms of branes. We discuss various properties of the asymptotically Godel black hole, including the physical bound on the rotation of the hole, the existence of closed timelike curves, and possible holographic protection of chronology.