  We consider hydrodynamics of N=4 supersymmetric SU(N_c) Yang-Mills plasma at
a nonzero density of R-charge. In the regime of large N_c and large 't Hooft
coupling the gravity dual description involves an asymptotically Anti- de
Sitter five-dimensional charged black hole solution of Behrnd, Cvetic and
Sabra. We compute the shear viscosity as a function of chemical potentials
conjugated to the three U(1) \subset SO(6)_R charges. The ratio of the shear
viscosity to entropy density is independent of the chemical potentials and is
equal to 1/4\pi. For a single charge black hole we also compute the thermal
conductivity, and investigate the critical behavior of the transport
coefficients near the boundary of thermodynamic stability.
