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Abstract The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential μ, despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite μ, and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should be better at μ > T than at μ = 0.