The Chandra Deep Field South ( CDF-S ) 1Ms exposure produced a catalog of 346 X-ray sources , of which 59 were not visible on the VLT/FORS1 and the ESO-MPI/WFI deep R -band images to a limit of R _ { vega } =26.1–26.7 mag . Using the first release of the ESO VLT/ISAAC JHK _ { s } data on the CDF-S , we identified six of the twelve such objects that were within the coverage of these IR observations . The VLT/FORS1 I -band data further confirms that five of these six objects are undetected in the optical . The photometric properties of these six counterparts are compared against those of the optically brighter counterparts of Chandra sources in the same field . We found that the location of these optically brighter Chandra sources in the near-IR color space was bifurcated , with the color of one branch being consistent with that of E/S0 galaxies at 0 \leq z \leq 1.5 and the other branch being consistent with that of unreddened AGN/QSOs at 0 \leq z \leq 3.5 . The six counterparts that we identified seemed to lie on the E/S0 branch and its extension , suggesting that these X-ray source hosts are mostly luminous E/S0 galaxies ( M _ { V } \sim - 20 mag in AB system ) at 1 \leq z \leq 2.5 . On the other hand , some of them can also be explained by AGN/QSOs over a wide redshift range ( 0 \leq z \leq 5 ) if a range of internal extinction ( A _ { V } = 0 –1 mag ) is allowed . However , the later interpretation requires fine-tuning extinction together with redshift for these objects individually . If they are indeed AGN/QSOs , the most luminous of them is just barely qualified for being a QSO . Finally , we point out that neither high-redshift ( z > 5 ) star-forming galaxies nor irregular galaxies at lower redshift can be a viable explanation to the nature of these six counterparts .