  The new state of matter produced at Relativistic Heavy Ion Collider reveals a
strongly coupled quark-gluon plasma with an extremely small shear viscosity to
entropy density ratio eta/s. We calculate the eta/s of an equilibrated hadron
matter characterized by a relativistic hadron resonance gas with a Hagedorn
mass spectrum that grows exponentially with the hadron mass. We find with
increase in temperature of the system the eta/s value decreases due to rapid
increase in the multiplicity of massive resonances. In the vicinity of the
critical temperature for deconfinement transition, the minimum value of eta/s
in the Hagedorn resonance gas is found to be consistent with the current
estimates for a strongly coupled quark-gluon plasma.
