  The shear viscosity coefficient of the one-component plasma is calculated
with unprecedented accuracy using equilibrium molecular dynamics simulations
and the Green-Kubo relation. Numerical and statistical uncertainties and their
mitigation for improving accuracy are analyzed. In the weakly coupled regime,
our the results agree with the Landau-Spitzer prediction. In the moderately and
strongly coupled regimes, our results are found in good agreement with recent
results obtained for the Yukawa one-component plasma using non-equilibrium
molecular dynamics. A practical formula is provided for evaluating the
viscosity coefficient across coupling regimes, from the weakly-coupled regime
up to solidification threshold. The results are used to test theoretical
predictions of the viscosity coefficients found in the literature.
