A suspension of nanoparticles in a linear polymer host is treated as a miscible polymer blend. The viscosity of the blend is calculated from a mixing rule as a linear combination of nanoparticle and diluted polymer melt viscosity contributions. For low molecular weights, below the entanglement value, the diluted polymer melt viscosity is taken from the Rouse model. For molecular weights much larger than the entanglement value, the diluted polymer viscosity is taken from the reptation model using the scaling analysis of Colby and Rubinstein. The theory predicts that for sufficiently high molecular weights, the viscosity increase due to nanparticle addition is compensated by dilution of the polymer by the nanoparticles. This results in a change in sign of the intrinsic viscosity from positive to negative as the molecular weight increases. The relaxation modulus for the entangled blends is also calculated using a tube model. The theoretical results are in good qualitative agreement with the experiments of Tuteja et al. (Tuteja, A.; Mackay, M. E.; Hawker, C. J.; Van Horn, B. Macromolecules 2005, 38, 8000) on crosslinked polystyrene nanoparticles in linear polystyrene.