A dimensionless measure of fluidity is the ratio of shear viscosity to entropy density. Experiments at the Relativistic Heavy Ion Collider (RHIC) indicate that the quark gluon plasma is a very good fluid, characterized by a value of eta/s close to the proposed quantum bound 1/(4*pi). Motivated by these results we study the fluidity of a cold Fermi gas in the unitary limit. We compute the shear viscosity in the high and low temperature limit, and analyze bounds on the shear viscosity that can be obtained from experiments on the hydrodynamics of cold atomic gases.