One of the key questions in observational cosmology is the identification of the sources responsible for ionization of the Universe after the cosmic ‘Dark Ages’, when the baryonic matter was neutral. The currently identified distant galaxies are insufficient to fully reionize the Universe by redshift z ≈ 6 (refs 1, 2, 3), but low-mass, star-forming galaxies are thought to be responsible for the bulk of the ionizing radiation. As direct observations at high redshift are difficult for a variety of reasons, one solution is to identify local proxies of this galaxy population. Starburst galaxies at low redshifts, however, generally are opaque to Lyman continuum photons. Small escape fractions of about 1 to 3 per cent, insufficient to ionize much surrounding gas, have been detected only in three low-redshift galaxies. Here we report far-ultraviolet observations of the nearby low-mass star-forming galaxy J0925+1403. The galaxy is leaking ionizing radiation with an escape fraction of about 8 per cent. The total number of photons emitted during the starburst phase is sufficient to ionize intergalactic medium material that is about 40 times as massive as the stellar mass of the galaxy.