The Kutateladze criterion for the pool boiling critical heat flux, which works well for nonmetallic liquids at or above atmospheric pressure, fails for the for the alkali liquid metals in the pressure range of interest for Liquid Metal Fast Breeder Reactor applications. In this pressure range bubble growth of the alkali liquid metals is largely inertia-controlled, in view of the large thermal conductivities, which implies a significant condensing heat flux within the bubbles themselves. The bubble growth is assumed to be described by the Mikic, Rohsenow, and Griffith equation. In this way a mean bubble age is determined, and hence a mean bubble thermal boundary layer thickness. The time-average critical heat flux is then obtained as the sum of the Kutateladze flux and the flux due to condensation on the bubble surfaces. No empirical parameters are employed. The present analysis predicts critical heat fluxes lying generally within the data band.