Only a handful of stars have been identified with an iron abundance [Fe/H]<-5, and only one at [Fe/H]<-7. These stars have very large carbon-to-iron ratios, with A(C)~7.0, most likely due to fallback in core-collapse supernovae, which makes their total metallicity Z much higher than their iron abundances. The failure to find population III stars, those with no metals, has been interpreted, with support from theoretical modeling, as the result of a top-heavy initial mass function. With zero or very low metal abundance limiting radiative cooling, the formation of low-mass stars could be inhibited. Currently, the star SDSS J1029+1729 sets the potential metallicity threshold for the formation of low-mass stars at log Z/Z_0~-5. We have identified SDSS J0023+0307, a primitive star with T_eff =6188+-84 K, and log g=4.9+-0.5, an upper limit [Fe/H]< -6.6, and a carbon abundance A(C)< 6.3. In our quest to push down the metallicity threshold we find J0023+0307 to be one of the two most iron-poor stars known, and it exhibits less carbon that most of stars at [Fe/H]< -5.