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The recently discovered Galactic halo star SDSS J102915+172927 (Caffau et al. 2011) has a mass less than 0.8 Msun and a metallicity of Z = 4.5 10^{-5} Zsun. We investigate the origin and properties of this star by reconstructing the physical conditions in its birth cloud. We show that the observed elemental abundance trend of SDSS J102915+172927 can be well fitted by the yields of core-collapse supernovae with metal-free progenitors of 20 Msun and 35 Msun. 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