  We consider corrections to the ratio of the shear viscosity to the entropy
density in strongly coupled nonabelian plasmas using the AdS/CFT
correspondence. In particular, higher derivative terms with the five-form RR
flux, which have been ignored in all previous calculations, are included. This
provides the first reliable calculation of the leading order correction in the
inverse 't Hooft coupling to the celebrated result eta/s=1/4pi. The leading
correction in inverse powers of the number of colours is computed. Our results
hold very generally for quiver gauge theories with an internal manifold L_pqr
in the holographic dual. Our analysis implies that the thermal properties of
these theories will not be affected by the five-form flux terms at this order.
