We study supersymmetric charged rotating black holes in AdS(5), and show th
at closed timelike curves occur outside the event horizon. Also upon liftin
g to rotating D3 brane solutions of type-IIB supergravity in ten dimensions
, closed timelike curves are still present. We believe that these causal an
omalies correspond to loss of unitarity in the dual N = 4,D = 4 super Yang-
Mills theory, i.e. the chronology protection conjecture in the AdS bulk is
related to unitarity bounds in the boundary CFT. We show that no charged or
uncharged geodesic can penetrate the horizon, so that the exterior region
is geodesically complete. These results still hold true in the quantum case
, i. e. the total absorption cross section for Klein-Gordon scalars propaga
ting in the black hole background is zero. This suggests that the effective
temperature is zero instead of assuming the naively found imaginary value.