  We compute shear viscosity and flavor diffusion coefficients for
ultra-relativistic gauge theory with many fermionic species, Nf >> 1, to
leading order in 1/Nf. The calculation is performed both at leading order in
the effective coupling strength g^2 Nf, using the Hard Thermal Loop (HTL)
approximation, and completely to all orders in g^2 Nf. This constitutes a
nontrivial test of how well the HTL approximation works. We find that in this
context, the HTL approximation works well wherever the renormalization point
sensitivity of the leading order HTL result is small.
