Near the horizon of a black brane solution in Anti-de Sitter space, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. For Einstein’s theory, the ratio of the shear viscosity of near-horizon metric fluctuations η to the entropy per unit of transverse volume s is η/s = 1/4π. We propose that, in generalized theories of gravity, this ratio is given by the ratio of two e...