  It is observed that three-dimensional G\"odel black holes can be promoted to
exact string theory backgrounds through an orbifold of an hyperbolic asymmetric
marginal deformation of the SL(2,R) WZW model. Tachyons are found in the
spectrum of long strings. Uplifting these solutions in type IIB supergravity,
extremal black holes are shown to preserve one supersymmetry in accordance with
the BTZ limit. We also make connections with some recently discussed warped
black hole solutions of topologically massive gravity, showing that they
actually correspond to quotients of spacelike squashed AdS_3.
