Improving the capabilities of detecting faint X-ray sources is fundamental to increase the statistics on faint high-z AGN and star-forming galaxies. The authors performed a simultaneous maximum likelihood point-spread function (PSF) fit in the 0.5-2 keV and 2-7 keV energy bands of the 4 Ms Chandra Deep Field South (CDFS) data at the position of the 34,930 CANDELS H-band selected galaxies. For each detected source, they provide X-ray photometry and optical counterpart validation. The authors validated this technique by means of a ray-tracing simulation, and detected a total of 698 X-ray point-sources with a likelihood L > 4.98 (i.e.> 2.7sigma). They show that the prior knowledge of a deep sample of Optical-NIR galaxies leads to a significant increase of the detection of faint (i.e. ~ 10^-17 erg s^-1 cm^-2 in the 0.5-2 keV band) sources with respect to "blind" X-ray detections. By including previous catalogs, this work increases the total number of X-ray sources detected in the 4 Ms CDFS, CANDELS area to 793, which represents the largest sample of extremely faint X-ray sources assembled to date. These results suggest that a large fraction of the optical counterparts of our X-ray sources determined by likelihood ratio actually coincides with the priors used for the source detection. Most of the newly detected sources are likely star-forming galaxies or faint absorbed AGN. The authors identified a few sources with putative photometric redshift z > 4. Despite the low number statistics, this sample significantly increases the number of X-ray selected candidate high-z AGN. The 4-Ms CDFS consists of 23 observations described in Table 1 of Luo et al. (2008, ApJS, 179, 19) plus 31 other pointings described in Xue et al. (2011, ApJS, 195, 10, hereafter X11) for a total exposure of ~4 Ms. For the purpose of this paper, the authors employed only observations taken with a focal temperature of <= -120 C, since at higher temperatures the background cannot be modeled with their technique. This table was created by the HEASARC in July 2016 based on <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJ/823/95">CDS Catalog J/ApJ/823/95</a> file catalog.dat. Some of the values for the name parameter in the HEASARC's implementation of this table were corrected in April 2018. This is a service provided by NASA HEASARC .