  We construct the general theory of first-order relativistic hydrodynamics for
a fluid exhibiting a chiral anomaly, including all possible viscous terms
allowed by symmetry. Using standard techniques, we compute the necessary and
sufficient conditions for this theory to be relativistically causal in the
nonlinear regime and for thermal equilibria to be linearly stable. This is the
first theory of first-order chiral hydrodynamics suitable for numerical
simulations.
