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) similar to 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 logZ/Z(circle dot) similar to -5. In our quest to push down the metallicity threshold 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. We find J0023+0307 to be one of the two most iron-poor stars known, and it exhibits less carbon that most of the stars at [Fe/H] < -5.