We present a comprehensive X-ray point source catalog of NGC 404 obtained as part of the Chandra Local Volume Survey. A new, 97 ks Chandra ACIS-S observation of NGC 404 was combined with archival observations for a total exposure of ~123 ks. Our survey yields 74 highly significant X-ray point sources and is sensitive to a limiting unabsorbed luminosity of ~6x10^35 erg s^-1 in the 0.35-8 keV band. To constrain the nature of each X-ray source, cross-correlations with multi-wavelength data were generated. We searched overlapping HST observations for optical counterparts to our X-ray detections, but find only two X-ray sources with candidate optical counterparts. We find 21 likely low mass X-ray binaries (LMXBs), although this number is a lower limit due to the difficulties in separating LMXBs from background AGN. The X-ray luminosity functions (XLFs) in both the soft and hard energy bands are presented. The XLFs in the soft band (0.5-2 keV) and the hard band (2-8 keV) have a limiting luminosity at the 90% completeness limit of 10^35 erg s^-1 and 10^36 erg s^-1, respectively, significantly lower than previous X-ray studies of NGC 404. We find the XLFs to be consistent with those of other X-ray populations dominated by LMXBs. However, the number of luminous (>10^37 erg s^-1) X-ray sources per unit stellar mass in NGC 404 is lower than is observed for other galaxies. The relative lack of luminous XRBs may be due to a population of LMXBs with main sequence companions formed during an epoch of elevated star formation ~0.5 Gyr ago.
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