  The Chandra Deep Field is the region of the sky with the highest
concentration of X-ray data available: 4Ms of Chandra and 3Ms of XMM data,
allowing excellent quality spectra to be extracted even for faint sources. We
take advantage of this in order to compile a sample of heavily obscured Active
Galactic Nuclei (AGN) using X-ray spectroscopy. We select our sample among the
176 brightest XMM sources, searching for either a) flat X-ray spectra (Photon
index<1.4 at the 90% confidence level) suggestive of a reflection dominated
continuum or b) an absorption turn-over suggestive of a column density higher
than ~10^{24} cm-2. We find a sample of nine candidate heavily obscured sources
satisfying the above criteria. Four of these show statistically significant
FeKalpha lines with large equivalent widths (three out of four have EW
consistent with 1 keV) suggesting that these are the most secure Compton-thick
AGN candidates. Two of these sources are transmission dominated while the other
two are most probably reflection dominated Compton-thick AGN. Although this
sample of four sources is by no means statistically complete, it represents the
best example of Compton-thick sources found at moderate-to-high redshift with
three sources at z=1.2-1.5 and one source at z=3.7. Using Spitzer and Herschel
observations, we estimate with good accuracy the X-ray to mid-IR (12 micron)
luminosity ratio of our sources. These are well below the average AGN relation,
independently suggesting that these four sources are heavily obscured.
