This catalog lists the X-ray point-source population in the nearby Virgo elliptical galaxy NGC 4636 from three Chandra X-ray observations. These observations, totaling ~193 ks after time filtering, were taken with the Advanced CCD Imaging Camera (ACIS) over a three-year period. Using a wavelet decomposition detection algorithm, the authors detected 318 individual point sources. For their analysis, they used a subset of 277 detections with >= net 10 counts (a limiting luminosity of approximately 1.2 x 10³⁷ erg s^-1 in the 0.5-2 keV band, outside the central 1.5 arcminutes bright galaxy core). This table contains this subset of 277 X-ray sources. The authors discuss the radial distribution of the point sources. Between 1.5 and 6 arcminutes from the center, 25% of the sources are likely to be background sources (active galactic nuclei (AGNs)) and 75% to be low-mass X-ray binaries (LMXBs) within the galaxy, while at radial distances greater than 6 arcminutes, background sources (AGN) will dominate the point sources. The authors explore short and long-term variability (over timescales of 1 day to three years) for X-ray point sources in this elliptical galaxy. 54 sources (24%) in the common ACIS fields of view show significant variability between observations. Of these, 37 are detected with at least 10 net counts in only one observation and thus may be "transient." In addition, ~10% of the sources in each observation show significant short-term variability. The cumulative luminosity function (LF) for the point sources in NGC 4636 can be represented as a power law of slope Alpha = 1.14 +/- 0.03. The authors do not detect, but estimate an upper limit of ~4.5 x 10³⁷ erg s^-1 to the current X-ray luminosity of, the historical supernova SN1939A. They find 77 matches between X-ray point sources and globular cluster (GC) candidates found in deep optical images of NGC 4636. In the annulus from 1.5 to 6 arcminutes of the galaxy center, 48 of the 129 X-ray point sources (37%) with >=10 net counts are matched with GC candidates. Since they expect 25% of these sources to be background AGN, the percentage matched with GCs could be as high as 50%. Of these matched sources, the authors find that ~70% are associated with the redder GC candidates, those that are thought to have near-solar metal abundance. The fraction of GC candidates with an X-ray point source match decreases with decreasing GC luminosity. The authors do not find a correlation between the X-ray luminosities of the matched point sources and the luminosity or color of the host GC candidates. The LFs of the X-ray point sources matched with GCs and those that are unmatched have similar slopes over 1.8 x 10³⁷ erg s^-1 <= L_x <= 1 x 10³⁸ erg s^-1. This table was created by the HEASARC in July 2009 based on electronic versions of Tables 2 and 3 from the paper obtained from the ApJ web site, but excluding the 7 entries in Table 3 which corresponded to weaker X-ray sources which were not listed in Table 2. 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 .