Evidence of very low metallicity and high ionization state in a strongly lensed, star-forming dwarf galaxy at z=3.417

We investigate the gas-phase metallicity and Lyman Continuum (LyC) escape fraction of a strongly gravitationally lensed, extreme emission-line galaxy at z=3.417, J1000+0221S, recently discovered by the CANDELS team. We derive ionization and metallicity sensitive emission-line ratios from H+K band LBT/LUCI medium resolution spectroscopy. J1000+0221S shows high ionization conditions, as evidenced by its enhanced [OIII]/[OII] and [OIII]/Hbeta ratios. Consistently, strong-line methods based on the available line ratios suggest that J1000+0221S is an extremely metal-poor galaxy, with a metallicity of 12+log(O/H) < 7.44 (< 5% solar), placing it among the most metal-poor star-forming galaxies at z > 3 discovered so far. In combination with its low stellar mass (2x10^8 Msun) and high star formation rate (5 Msun/yr), the metallicity of J1000+0221S is consistent with the extrapolation to low masses of the mass-metallicity relation traced by Lyman-break galaxies at z > 3, but it is 0.55 dex lower than predicted by the fundamental metallicity relation at z < 2.5. These observations suggest the picture of a rapidly growing galaxy, possibly fed by the massive accretion of pristine gas. Additionally, deep LBT/LBC in the UGR bands are used to derive a limit to the LyC escape fraction, thus allowing us to explore for the first time the regime of sub-L* galaxies at z > 3. We find a 1sigma upper limit to the escape fraction of 23%, which adds a new observational constraint to recent theoretical models predicting that sub-L* galaxies at high-z have high escape fractions and thus are the responsible for the reioization of the Universe.