The two known “ hyper-metal-poor ” ( HMP ) stars , HE0107-5240 and HE1327-2326 , have extremely high enhancements of the light elements C , N , and O relative to Fe and appear to represent a statistically significant excess population relative to the halo metallicity distribution extrapolated from [ Fe/H ] > -3 . This study weighs the available evidence for and against three hypothetical origins for these stars : ( 1 ) that they formed from gas enriched by a primordial “ faint supernova ” , ( 2 ) that they formed from gas enriched by core-collapse supernovae and C-rich gas ejected in rotation-driven winds from massive stars , and ( 3 ) that they formed as the low-mass secondaries in binary systems at Z \sim 10 ^ { -5.5 } Z _ { \odot } and acquired their light-element enhancements from an intermediate-mass companion as it passed through an AGB phase . The observations interpreted here , especially the depletion of lithium seen in HE1327-2326 , favor the binary mass-transfer hypothesis . If HE0107-5240 and HE1327-2326 formed in binary systems , the statistically significant absence of isolated and/or C-normal stars at similar [ Fe/H ] implies that low-mass stars could form at that metallicity , but that masses M \lesssim 1.4 M _ { \odot } were disfavored in the IMF . This result is also explained if the abundance-derived top-heavy IMF for primordial stars persists to [ Fe/H ] \sim - 5.5 . This finding indicates that low-mass star formation was possible at extremely low metallicity , and that the typical stellar mass may have had a complex dependence on metallicity rather than a sharp transition driven solely by gas cooling .