We present a new catalog of TeV gamma-ray sources using 1523 days of data from the High-Altitude Water Cherenkov (HAWC) Observatory. The catalog represents the most sensitive survey of the northern gamma-ray sky at energies above several TeV, with three times the exposure compared to the previous HAWC catalog, 2HWC. We report 65 sources detected at >=5{sigma} significance, along with the positions and spectral fits for each source. The catalog contains eight sources that have no counterpart in the 2HWC catalog, but are within 1{deg} of previously detected TeV emitters, and 20 sources that are more than 1{deg} away from any previously detected TeV source. Of these 20 new sources, 14 have a potential counterpart in the fourth Fermi Large Area Telescope catalog of gamma-ray sources. We also explore potential associations of 3HWC sources with pulsars in the Australia Telescope National Facility (ATNF) pulsar catalog and supernova remnants in the Galactic supernova remnant catalog.

Cone search capability for table J/ApJ/905/76/sources (Source list and nearest TeVCat sources (Table 1) and radius, best-fit spectrum, and energy range (Table 2))

Cone search capability for table J/ApJ/905/76/table3 (New HAWC sources with no TeV counterpart)

Cone search capability for table J/ApJ/905/76/table4 (HAWC sources with the corresponding TeV halo candidate pulsars within 1deg)