Summary: We consider hydrodynamics of \(\mathcal N = 4\) supersymmetric \(SU(N_{c})\) Yang-Mills plasma at a nonzero density of \(R\)-charge. In the regime of large \(N_{c}\) and large ’t Hooft coupling the gravity dual description involves an asymptotically Anti-de Sitter five-dimensional charged black hole solution of K. Behrnd, M. Cvetič and W. A. Sabra [Nucl. Phys., B 553, No. 1–2, 317–332 (1999; Zbl 0949.83072)]. We compute the shear viscosity as a function of chemical potentials conjugated to the three \(U(1)\subset SO(6)_{R}\) charges. The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to \(1/4\pi \). For a single charge black hole we also compute the thermal conductivity, and investigate the critical behavior of the transport coefficients near the boundary of thermodynamic stability.