We present Chandra and Spitzer data for the 186, extragalactic, hard 2-10keV X-ray selected sources, which lie in the central part of the Chandra Deep Field South (CDFS). For the vast majority of sources (99.5%), there is a spectroscopic or photometric redshift available. We classify 17 sources as X-ray obscured QSOs, strictly according to X-ray criteria, i.e. defined as having large hydrogen column densities (NH>10^22cm^-2^) and luminosities (LX>10^44^erg/s). The surface density of X-ray obscured QSOs is ~210{deg}^-2^. We find 18 candidate Compton-thick NH>10^24^cm^-2^ sources, of which three have QSO luminosities (LX>10^44^erg/s). The X-ray obscured QSO comprise a mixed bag of objects, covering the redshift range z=1.3-4.3. Eight of these show narrow-line optical spectra, two show no obscuration in their optical spectra that present broad lines, while for the other seven there is only a photometric redshift available. About half of the X-ray obscured QSOs show high X-ray to optical flux ratios, X/O>1, and red colours, I-3.6{mu}m>4. Combining the X-ray with the mid-IR 8{mu}m or 24{mu}m flux can be used as an additional diagnostic to sift out the heavily obscured AGN. All X-ray selected QSOs present red mid-IR colours and can be easily separated among mid-IR sources, demonstrating that mid-IR selection provides a powerful tool for detecting obscured QSOs.