An extreme [OIII] emitter at $z=3.2$: a low metallicity Lyman continuum
  source
  [Abridged] We investigate the physical properties of a Lyman continuum
emitter candidate at $z=3.212$ with photometric coverage from $U$ to MIPS
24$\mu$m band and VIMOS/VLT and MOSFIRE/Keck spectroscopy. Investigation of the
UV spectrum confirms a direct spectroscopic detection of the Lyman continuum
emission with $S/N>5$. Non-zero Ly$\alpha$ flux at the systemic redshift and
high Lyman-$\alpha$ escape fraction suggest a low HI column density. The weak C
and Si low-ionization absorption lines are also consistent with a low covering
fraction along the line of sight. The
[OIII]$\lambda\lambda4959,5007+\mathrm{H}\beta$ equivalent width is one of the
largest reported for a galaxy at $z>3$
($\mathrm{EW}([\mathrm{OIII}]\lambda\lambda4959,5007+\mathrm{H}\beta) \simeq
1600\AA$, rest-frame) and the NIR spectrum shows that this is mainly due to an
extremely strong [OIII] emission. The large observed [OIII]/[OII] ratio ($>10$)
and high ionization parameter are consistent with prediction from
photoionization models in case of a density-bounded nebula scenario.
Furthermore, the
$\mathrm{EW}([\mathrm{OIII}]\lambda\lambda4959,5007+\mathrm{H}\beta)$ is
comparable to recent measurements reported at $z\sim7-9$, in the reionization
epoch. We also investigate the possibility of an AGN contribution to explain
the ionizing emission but most of the AGN identification diagnostics suggest
that stellar emission dominates instead. This source is currently the first
high-$z$ example of a Lyman continuum emitter exhibiting indirect and direct
evidences of a Lyman continuum leakage and having physical properties
consistent with theoretical expectation from Lyman continuum emission from a
density-bounded nebula.
