  We compute the strong coupling limit of the shear viscosity for the N=4
super-Yang-Mill theory with a chemical potential. We use the five-dimensional
Reissner-Nordstrom-anti-deSitter black hole, so the chemical potential is the
one for the R-charges U(1)_R^3. We compute the quasinormal frequencies of the
gravitational and electromagnetic vector perturbations in the background
numerically. This enables one to explicitly locate the diffusion pole for the
shear viscosity. The ratio of the shear viscosity eta to the entropy density s
is eta/s=1/(4pi) within numerical errors, which is the same result as the one
without chemical potential.
