A micromechanical model for the zero shear viscosity of polyampholyte-stabilized colloidal dispersions based on the osmotic overlap potential is proposed and tested against model system measurements. This model relates the shear viscosity of polyampholyte-stabilized colloidal dispersions to the oncotic pressure of polyampholyte solutions through an interparticle potential and an effective hard-sphere scaling. The results of viscosity calculations based on independently measured parameters compare favorably to experimental measurements on model, silica dispersions stabilized with adsorbed photographic grade gelatin. The results support a direct link between the capacity of polyampholytes and polyelectrolytes to stabilize dispersions and control dispersion viscosity and their solution oncotic pressure. The model is also demonstrated to provide a master curve for literature data for the zero shear viscosity of polyampholyte stabilized colloidal dispersions.