  We determine a next-to-leading order result for the shear channel thermal
spectral function in SU(N) Yang-Mills theory, working in the limit of vanishing
external three-momentum. The result is subsequently applied to the evaluation
of the corresponding imaginary time correlator, and its use in the context of
sum rules is discussed. Our hope is that the calculation will eventually find
use in the nonperturbative determination of the shear viscosity of the theory.
