We study the escape of Lyman continuum radiation from the disks of dwarf starburst galaxies, with and without supershells, by solving the radiation transfer problem of stellar radiation through them. We model disks with M d ¼ 10 8 10 10 M , with exponential surface density profiles as a function of redshift, and model the effects of repeated supernova explosions driving supershells out of the disks, using the hydrodynamic simulation code ZEUS-3D. The amount of star formation is assumed proportional to mass above some density threshold. We vary the threshold to explore the range of star formation efficiencies, f à ¼ 0:006, 0.06, and 0.6. We find that the interstellar gas swept up in dense supershells can effectively trap the ionizing photons before the supershells blow out of the disks. The blowouts then create galactic outflows, chimneys that allow the photons to escape directly to the intergalactic medium. Our results are consistent with escape fractions of less than 0.1 measured in local dwarf starburst galaxies, because they are likely observed while the starbursts are young, before blowout. We suggest that high-redshift dwarf starburst galaxies may make a substantial contribution to the UV background radiation with total escape fractions e0.2, as expected if star formation efficiencies are e0:06.