A theoretical model is developed to predict the critical heat flux (CHF) limit for saturated pool boiling on the outer surface of a heated hemispherical vessel. The model considers the existence of a microlayer underneath an elongated vapor slug on a downward facing curved healing surface. The micro-layer is treated as a thin liquid film with numerous micro-vapor jets penetrating it. The micro-jets have the characteristic size dictated by Helmholtz instability. Local dryout is considered to occur when the supply of fresh liquid from the two-phase boundary layer to the micro-layer is not sufficient to prevent depletion of the liquid film by boiling. A boundary layer analysis, treating the two-phase motion as an external buoyancy-driven flow, is performed to determine the liquid supply rate and thus the local critical heat flux. The model provides a clear physical explanation for the spatial variation of the CHF observed in experiments and for the weak dependence of the CHF data on the physical size of the vessel.