  In this work the shear viscosity of strongly interacting matter is calculated
within a two-flavor Nambu--Jona-Lasinio model as a function of temperature and
chemical potential. The general Kubo formula is applied, incorporating the full
Dirac structure of the thermal quark spectral function and avoiding commonly
used on-shell approximations. Mesonic fluctuations contributing via Fock
diagrams provide the dominant dissipative processes. The resulting ratio
$\eta/s$ (shear viscosity over entropy density) decreases with temperature and
chemical potential. Interpolating between our NJL results at low temperatures
and hard-thermal-loop results at high temperatures a minimum slightly above the
AdS/CFT benchmark $\eta/s=1/4\pi$ is obtained.
