The results of new detailed two-dimensional radiation-hydrodynamical calculations of the effects of radiation-driven shock waves from two O stars on inhomogeneities embedded in molecular clouds are presented. The calculations indicate that neutral primordial clumps of gas with 84 solar masses can be highly compressed in 30,000 yr with density enhancements greater than 170 over ambient densities and 40 solar masses remaining. Inhomogeneities that are compressed in this manner by stars in the range O7-B0 survive ionization evaporation and may rapidly form new stars. Low-mass objects would not survive, and there would be a natural cutoff of low-mass and high-mass stars. A scenario is presented for hierarchical radiation-driven implosion as a potential, new, highly efficient mechanism for star formation that may explain aspects of recent observations of new star formation in ultracompact H II regions.