  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.
