An analytic model for the slowing down of polymer chain diffusion in nanocomposites attributable to excluded volume effects is presented. The nanocomposite is modeled as an ensemble of cylinders through which the polymer chains diffuse. The reduction of polymer diffusion in each cylinder is equated with the reduction of diffusion for a sphere through a cylinder. The distribution of cylinder diameters within the ensemble is determined from statistical mechanical theories based on the packing of spherical particles. For low loadings of spherical particles in nanocomposites, this model results in a master curve for the reduced diffusion coefficient. With no adjustable parameters, the model agrees with recent data for tracer diffusion measurements in polymer nanocomposites at low loading.