A closed-form analytical model has been developed to estimate the effect of a nonuniform surface charge distribution on the potential of mean force between two plates or two spherical colloidal particles. This model is an extension for randomly charged surfaces of the well-known Hogg-Healy-Fuerstenau model. The surface charge distribution is random, and we characterize this by defining (1) N equal-area regions on the surfaces, (2) an average surface potential (< zeta >), and (3) a standard deviation of surface potential (alpha (zeta)) among the regions. The model predicts that the standard deviation of the potential of mean force (alpha (Phi)) at any gap distance is approximately proportional to sigma (zeta)/rootN. The practicality of the model derives from the fact that sigma (zeta)/rootN is experimentally measurable. Charge nonuniformity provides one explanation for why classical colloidal stability theory often fails. In addition, since regions with a low charge density tend to be more hydrophobic, charge nonuniformity might allow strong hydrophobic interactions between particles.