  We compute the shear viscosity in the O(N) model at first nontrivial order in
the large N expansion. The calculation is organized using the 1/N expansion of
the 2PI effective action (2PI-1/N expansion) to next-to-leading order, which
leads to an integral equation summing ladder and bubble diagrams. We also
consider the weakly coupled theory for arbitrary N, using the three-loop
expansion of the 2PI effective action. In the limit of weak coupling and
vanishing mass, we find an approximate analytical solution of the integral
equation. For general coupling and mass, the integral equation is solved
numerically using a variational approach. The shear viscosity turns out to be
close to the result obtained in the weak-coupling analysis.
