  We prove that ideal chiral hydrodynamics, as derived from chiral kinetic
theory, is acausal and its initial-value problem is ill-posed both in the
linearized case around a local equilibrium solution and also in the full
nonlinear regime. Therefore, such theory cannot be used to determine how the
chiral anomaly affects the hydrodynamic evolution. We show that these
fundamental issues can be fixed by using different definitions (frames) for the
hydrodynamic fields. This leads to a causal theory of ideal chiral
hydrodynamics where the vorticity strength is constrained by the coefficient
that encodes the anomaly.
