  We compute the shear viscosity of a superfluid atomic Fermi gas in the
unitarity limit. The unitarity limit is characterized by a divergent scattering
length between the atoms, and it has been argued that this will result in a
very small viscosity. We show that in the low temperature T limit the shear
viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the
chemical potential and the Fermi energy, mu=xi E_F. Combined with the high
temperature expansions of the viscosity our results suggest that the viscosity
has a minimum near the critical temperature T_c. A naive extrapolation
indicates that the minimum value of the ratio of viscosity over entropy density
is within a factor of ~ 5 of the proposed lower bound hbar/(4\pi k_B).
