We present an analysis of the Ultraviolet and Visual Echelle Spectrograph (UVES) high-resolution spectroscopic observations at the 8.2 m Very Large Telescope of J0023+0307, a main-sequence 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 fallback 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. Based on observations made with Very Large Telescope (VLT) at Paranal Observatory, Chile.