  We derive the set of inequalities that is necessary and sufficient for
nonlinear causality and linear stability of first-order relativistic
hydrodynamics with either a $U(1)_V$ conserved current or a $U(1)_A$ current
with a chiral anomaly or both. Our results apply to generic hydrodynamic frames
in which no relations among the transport parameters are imposed. Furthermore,
our analysis yields, to the best of our knowledge, the first theory of viscous
chiral hydrodynamics proven to be causal and stable. We find that causality
demands the absence of vorticity-induced heat flux, forcing a departure from
the thermodynamic frame in the chiral case. The inequalities for causality and
stability define a hypervolume in the space of transport parameters, wherein
each point corresponds to a consistent formulation. Notably, causality is
determined by just three combinations of transport parameters. We present our
results in a form amenable to numerical hydrodynamic simulations.
