We present Chandra and Spitzer data for the 186, extragalactic, hard 2-10 keV 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 (N-H > 10(22) cm(-2)) and luminosities (L-x > 10(44) erg s(-1)). The surface density of X-ray obscured QSOs is similar to 210 deg(-2). We find 18 candidate Compton-thick N-H > 10(24) cm(-2) sources, of which three have QSO luminosities (L-x > 10(44) erg s(-1)). 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.