  We investigate the shear viscosity of a pion gas in relativistic kinetic
theory, using the Nambu-Jona-Lasinio model to construct the pion mass and the
pi-pi interaction at finite temperature. Whereas at low temperatures the
scattering properties and, hence, the viscosity are in agreement with
lowest-order chiral perturbation theory, we find strong medium modifications in
the crossover region. Here the system is strongly coupled and the scattering
lengths diverge, similarly as for ultra-cold Fermi gases at a Feshbach
resonance. As a consequence, the ratio eta/s is found to be strongly reduced as
compared to calculations without medium-modified masses and scattering
amplitudes. However, the quantitative results are very sensitive to the details
of the applied approximations.
