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 (NH>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 (NH>~10^25 cm^-2), intrinsically luminous (L(2-10keV)>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{μ}m luminosity ratios, agree on the fact that the nuclear emission must be suppressed by a 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~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. ; Comment: 6 pages, 3 figures. Accepted for publication in A&A