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 , J 1000 + 0221 S , recently discovered by the CANDELS team . We derive ionization and metallicity sensitive emission-line ratios from H+K band LBT/LUCI medium resolution spectroscopy . J 1000 + 0221 S shows high ionization conditions , as evidenced by its enhanced [ O iii ] / [ O ii ] and [ O iii ] /H \beta ratios . Consistently , strong-line methods based on the available line ratios suggest that J 1000 + 0221 S is an extremely metal-poor galaxy , with a metallicity of 12 + \log ( O/H ) < 7.44 ( Z < 0.05 Z _ { \odot } , placing it among the most metal-poor star-forming galaxies at z \gtrsim 3 discovered so far . In combination with its low stellar mass ( 2 \times 10 ^ { 8 } M _ { \odot } ) and high star formation rate ( 5 M _ { \odot } yr ^ { -1 } ) , the metallicity of J 1000 + 0221 S is consistent with the extrapolation to low masses of the mass-metallicity relation traced by Lyman-break galaxies at z \gtrsim 3 , but it is 0.55 dex lower than predicted by the fundamental metallicity relation at z \lesssim 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 1 \sigma 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 .