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.