  We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation
Theory at low and moderate temperatures, below any phase transition to a
quark-gluon plasma phase. We argue that inelastic processes are irrelevant and
exponentially suppressed at low temperatures. Since the system falls out of
chemical equilibrium upon expansion,a pion chemical potential must be
introduced, so we extend the existing theory to include it. We control the zero
modes of the collision operator and Landau's conditions of fit when solving the
Boltzmann equation with the elastic collision kernel. The dependence of the
bulk viscosity with temperature is reminiscent of the findings of
Fernandez-Fraile and Gomez Nicola, while the numerical value is closer to that
of Davesne. In the zero-temperature limit we correctly recover the vanishing
viscosity associated to a non-relativistic monoatomic gas.
