  Kovtun, Son and Starinets have conjectured that the viscosity to entropy
density ratio $\eta/s$ is always bounded from below by a universal multiple of
$\hbar$ i.e., $\hbar/(4\pi k_{B})$ for all forms of matter. Mysteriously, the
proposed viscosity bound appears to be saturated in all computations done
whenever a supergravity dual is available. We consider the near horizon limit
of a stack of M2-branes in the grand canonical ensemble at finite R-charge
densities, corresponding to non-zero angular momentum in the bulk. The
corresponding four-dimensional R-charged black hole in Anti-de Sitter space
provides a holographic dual in which various transport coefficients can be
calculated. We find that the shear viscosity increases as soon as a background
R-charge density is turned on. We numerically compute the few first corrections
to the shear viscosity to entropy density ratio $\eta/s$ and surprisingly
discover that up to fourth order all corrections originating from a non-zero
chemical potential vanish, leaving the bound saturated. This is a sharp signal
in favor of the saturation of the viscosity bound for event horizons even in
the presence of some finite background field strength. We discuss implications
of this observation for the conjectured bound.
