  We determine viscosity corrections to the retarded, advanced and symmetric
gluon self energies and to the static propagator in the weak-coupling "hard
loop" approximation to high-temperature QCD. We apply these results to
calculate the imaginary part of the heavy-quark potential which is found to be
smaller (in magnitude) than at vanishing viscosity. This implies a smaller
decay width of quarkonium bound states in an anisotropic plasma.
