The low shear viscosity eta of a nondilute polymer solution is calculated from an extended Kirkwood-Riseman model that includes hydrodynamic interactions between chains. Hydrodynamic interaction tensors for chains in a weak shear field are obtained for interacting pairs and trios of chains. The model proposed here gives a general expansion for eta(c) to arbitrary order in polymer concentration c. Divergent integrals encountered in some prior calculations using Stokes-level hydrodynamics are avoided. The model confirms empirical demonstrations that the intrinsic viscosity [eta] is a good reducing variable for eta(c).