The shear viscosity to entropy ratio (eta/s) is estimated for the hot and dense QCD matter created in Au+Au collisions at BNL Relativistic Heavy Ion Collider (square root[s_{NN}]=200 GeV). A very low value is found; eta/s approximately 0.1, which is close to the conjectured lower bound (1/4pi). It is argued that such a low value is indicative of thermodynamic trajectories for the decaying matter which lie close to the QCD critical end point.