  We prove that ideal chiral hydrodynamics, as derived from chiral kinetic
theory, is acausal and its initial-value problem is ill-posed. Therefore, such
theory cannot be used to determine how the chiral anomaly affects the
hydrodynamic evolution. We also prove that the standard first-order theory of
viscous chiral hydrodynamics is acausal. We show that these fundamental issues
can be cured by using different definitions (frames) for the hydrodynamic
fields.
