  Gauge theory-string theory duality describes strongly coupled N=4
supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near
extremal black 3-brane geometry in type IIB string theory. We use this
correspondence to compute the leading correction in inverse 't Hooft coupling
to the shear diffusion constant, bulk viscosity and the speed of sound in the
large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients
are extracted from the dispersion relation for the shear and the sound wave
lowest quasinormal modes in the leading order alpha'-corrected black D3 brane
geometry. We find the shear viscosity extracted from the shear diffusion
constant to agree with result of [hep-th/0406264]; also, the leading correction
to bulk viscosity and the speed of sound vanishes. Our computation provides a
highly nontrivial consistency check on the hydrodynamic description of the
alpha'-corrected nonextremal black branes in string theory.
