We present an analysis of the UVES high-resolution spectroscopic observations at the 8.2m VLT of J0023+0307, an extremely iron-poor dwarf star. We are unable to detect iron lines in the spectrum but derive [Fe/H]< −6.1 from the Ca II resonance lines assuming [Ca/Fe]=0.40. The chemical abundance pattern of J0023+0307, with very low [Fe/Mg] and [Ca/Mg] abundance ratios, but relatively high absolute Mg and Si abundances, suggests J0023+0307 is a second generation star formed from a molecular cloud polluted by only one supernova in which the fall-back mechanism played a role. We measure a carbon abundance of A(C) = 6.2 that places J0023+0307 on the “low” band in the A(C)−[Fe/H] diagram, suggesting no contamination from a binary companion. This star is also unique having a lithium abundance (A(Li)=2.02±0.08) close to the level of the Lithium Plateau, in contrast with lower Li determinations or upper limits in all other extremely iron-poor stars. The upper envelope of the lithium abundances in unevolved stars spanning more than three orders of magnitude in metallicity (−6 <[Fe/H]< −2.5) defines a nearly constant value. We argue that it is unlikely that such uniformity is the result of depletion processes in stars from a significantly higher initial Li abundance, but suggests instead a lower primordial production, pointing to new physics such as decaying massive particles, varying fundamental constants, or nuclear resonances, that could have affected the primordial 7Li production.