We report the discovery and high-resolution , high S / N , spectroscopic analysis of the ultra-metal-poor red giant HE 0557 - 4840 , which is the third most heavy-element deficient star currently known . Its atmospheric parameters are T _ { \mbox { \scriptsize eff } } = 4900 K , \log g = 2.2 , and [ Fe/H ] = –4.75 . This brings the number of stars with [ Fe/H ] < –4.0 to three , and the discovery of HE 0557 - 4840 suggests that the metallicity distribution function of the Galactic halo does not have a “ gap ” between [ Fe/H ] = –4.0 , where several stars are known , and the two most metal-poor stars , at [ Fe/H ] \sim –5.3 . HE 0557 - 4840 is carbon rich – [ C/Fe ] = +1.6 – a property shared by all three objects with { [ Fe / H ] } < -4.0 , suggesting that the well-known increase of carbon relative to iron with decreasing [ Fe/H ] reaches its logical conclusion – ubiquitous carbon richness – at lowest abundance . We also present abundances ( nine ) and limits ( nine ) for a further 18 elements . For species having well-measured abundances or strong upper limits , HE 0557 - 4840 is “ normal ” in comparison with the bulk of the stellar population at [ Fe/H ] \sim –4.0 – with the possible exception of Co. We discuss the implications of these results for chemical enrichment at the earliest times , in the context of single ( “ mixing and fallback ” ) and two-component enrichment models . While neither offers a clear solution , the latter appears closer to the mark . Further data are required to determine the oxygen abundance and improve that of Co , and hence more strongly constrain the origin of this object .