  The fireball concept of Rolf Hagedorn, developed in the 1960's, is an
alternative description of hadronic matter. Using a recently derived mass
spectrum, we use the transport model GiBUU to calculate the shear viscosity of
a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo
calculations. Since the entropy density is rising ad infinitum near $T_H$, this
leads to a very low shear viscosity to entropy density ratio near $T_H$.
Further, by comparing our results with analytic expressions, we find a nice
extrapolation behavior, indicating that a gas of Hagedorn states comes close or
even below the boundary $1/4\pi$ from AdS-CFT.
