  The existence of a large population of Compton thick (CT, $N_{H}>10^{24}
cm^{-2}$) AGN is a key ingredient of most Cosmic X-ray background synthesis
models. However, direct identification of these sources, especially at high
redshift, is difficult due to the flux suppression and complex spectral shape
produced by CT obscuration. We explored the Chandra COSMOS Legacy point source
catalog, comprising 1855 sources, to select via X-ray spectroscopy, a large
sample of CT candidates at high redshift. Adopting a physical model to
reproduce the toroidal absorber, and a Monte-Carlo sampling method, we selected
67 individual sources with >5% probability of being CT, in the redshift range
$0.04<z<3.5$. The sum of the probabilities above $N_{H}>10^{24} cm^{-2}$, gives
a total of 41.9 effective CT, corrected for classification bias. We derive
number counts in the 2-10 keV band in three redshift bins. The observed
logN-logS is consistent with an increase of the intrinsic CT fraction
($f_{CT}$) from $\sim0.30$ to $\sim0.55$ from low to high redshift. When
rescaled to a common luminosity (log(L$_{\rm X}$/erg/s)$=44.5$) we find an
increase from $f_{CT}=0.19_{-0.06}^{+0.07}$ to $f_{CT}=0.30_{-0.08}^{+0.10}$
and $f_{CT}=0.49_{-0.11}^{+0.12}$ from low to high z. This evolution can be
parametrized as $f_{CT}=0.11_{-0.04}^{+0.05}(1+z)^{1.11\pm0.13}$. Thanks to
HST-ACS deep imaging, we find that the fraction of CT AGN in
mergers/interacting systems increases with luminosity and redshift and is
significantly higher than for non-CT AGN hosts.
