Highly obscured active galactic nuclei ( AGN ) are common in nearby galaxies , but are difficult to observe beyond the local Universe , where they are expected to significantly contribute to the black hole accretion rate density . Furthermore , Compton-thick ( CT ) absorbers ( N _ { H } \buildrel > \over { \sim } 10 ^ { 24 } cm ^ { -2 } ) suppress even the hard X-ray ( 2-10 keV ) AGN nuclear emission , and therefore the column density distribution above 10 ^ { 24 } cm ^ { -2 } is largely unknown . We present the identification and multi-wavelength properties of a heavily obscured ( N _ { H } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { 25 } cm ^ { -2 } ) , intrinsically luminous ( L _ { 2 - 10 } > 10 ^ { 44 } erg s ^ { -1 } ) AGN at z = 0.353 in the COSMOS field . Several independent indicators , such as the shape of the X-ray spectrum , the decomposition of the spectral energy distribution and X-ray/ [ NeV ] and X-ray/ 6 \mu m luminosity ratios , agree on the fact that the nuclear emission must be suppressed by a \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { 25 } cm ^ { -2 } column density . The host galaxy properties show that this highly obscured AGN is hosted in a massive star-forming galaxy , showing a barred morphology , which is known to correlate with the presence of CT absorbers . Finally , asymmetric and blueshifted components in several optical high-ionization emission lines indicate the presence of a galactic outflow , possibly driven by the intense AGN activity ( L _ { Bol } / L _ { Edd } = 0.3 - 0.5 ) . Such highly obscured , highly accreting AGN are intrinsically very rare at low redshift , whereas they are expected to be much more common at the peak of the star formation and BH accretion history , at z \sim 2 - 3 . We demonstrate that a fully multi-wavelength approach can recover a sizable sample of such peculiar sources in large and deep surveys such as COSMOS .