Low-shear viscosities have been studied for isotropic dispersions of uncharged colloidal silica rods in cyclohexane as a function of volume fraction Phi and aspect ratio r(p). Intrinsic viscosities in the limit Phi-->O agree with theoretical results [Brenner, H., Int. J. Multiphase Flow 1, 195 (1974)] for colloidal cylinders. The Phi(2) term in the low-shear viscosity, accounting for two-particle interactions, is considerably larger than predicted by D. H. Berry and W. B. Russel [J. Fluid Mech. 180, 475 (1987)] for dilute hard-rod dispersions. The discrepancy is very likely due to weak interparticle attractions, which also account for the novel observation of an isotropic-isotropic phase separation in the silica rod dispersions. Our results demonstrate that, in comparison to spheres, high aspect ratios markedly increase both the shear viscosity and its sensitivity to even minor attractions.