Using Chandra archive data, the authors conducted a thorough survey of luminous X-ray sources. They directly analyzed about 9400 Chandra ACIS observations and cross-correlated the detected X-ray sources with 77,000 galaxies within a distance of 250 Mpc. The final catalog includes 119 unique luminous X-ray source candidates with L_X > 3 x 10⁴⁰ erg/s from 93 galaxies or 41 HLX candidates with L_X > 1 x 10⁴¹ erg/s from 35 galaxies. The authors derive a moderate contamination rate due to foreground or background sources. In the reference paper, they also cross-correlate the catalog with FIRST, perform variability and periodicity tests, and analyze one HLX candidate in particular. This catalog could be a starting point to perform follow-up observations. In order to know whether an X-ray source falls within a particular galaxy, for each galaxy, the authors collected its center's RA, Dec, distance, and D₂₅ isophotal info, which includes major axis length, minor axis length, and the position angle of the major axis from the PGC2003 Catalog (Paturel et al. 2003, A&A, 412, 45), which includes the full RC3 catalog and has all of the necessary parameters except for distance. The authors restricted the minimum major axis length to be 10 arcseconds, and collected their distances from NED as much as possible. Their final sample includes 77,000 galaxies within 250 Mpc. The authors used all of the Chandra ACIS data in TE mode that were released before 2014, which includes 9400 ObsIDs. A roughly linear relation between the flux and count rate derived by PIMMS 4.6b was established assuming a power-law spectral shape and galactic foreground extinction (Kalberla et al. 2005, A&A, 440, 775). Any source with a PIMMS luminosity larger than 5 x 10³⁹ erg s^-1 would be recalculated by the CIAO script model flux assuming a power-law index of 1.7 in the 0.3 - 8.0 keV energy band. After the recalculation, 1,809 X-ray sources with L_x > 3 x 10⁴⁰ erg s^-1 falling within 640 D₂₅ contours covered by 905 ObsIDs were picked out. A large fraction of the 1,809 sources are galactic nuclei and some of them are repeated. Only off-nuclear sources are considered in this paper. In addition, the centers of the galaxies given by PGC2003 are not necessarily precise and the specific environments of the 1,809 sources are different. Therefore, the authors visually checked the Chandra and DSS images simultaneously, since two-band inspection can help to exclude the nuclear sources, bright knots, and extended sources. X-ray sources with clear DSS features would be dropped because, for a source with a visual magnitude <20 and a distance >30 Mpc, its absolute magnitude would be brighter than -12.4, which is beyond the limit of the brightest star clusters. This table was created by the HEASARC in February 2017 based on <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJS/222/12">CDS Catalog J/ApJS/222/12</a> file table1.dat, the list of very luminous X-ray source candidates found within the D₂₅ ellipses of Chandra ACIS-observed PGC2003 galaxies lying within 250 Mpc. 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 .