  We study the structure of closed timelike curves (CTCs) for the near horizon
limit of the five dimensional BMPV black hole, in its overrotating regime. We
argue that Bousso's holographic screens are inside the chronologically safe
region, extending a similar observation of Boyda et al. hep-th/0212087 for
Goedel type solutions. We then extend this result to quite generic axisymmetric
spacetimes with CTCs, showing that causal geodesics can't escape the
chronologically safe region. As a spin-off of our results, we fill a gap in the
identification of all maximally supersymmetric solutions of minimal five
dimensional supergravity, bringing this problem to a full conclusion.
