  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{\mu}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.
