We present the unWISE Catalog, containing the positions and fluxes of roughly 2 billion objects observed by the Wide-field Infrared Survey Explorer (WISE) over the full sky. The unWISE Catalog has two advantages over the existing WISE catalog (AllWISE): first, it is based on significantly deeper imaging, and second, it features improved modeling of crowded regions. The deeper imaging used in the unWISE Catalog comes from the coaddition of all publicly available 3-5um WISE imaging, including that from the ongoing NEOWISE-reactivation mission, thereby increasing the total exposure time by a factor of 5 relative to AllWISE. At these depths, even at high Galactic latitudes, many sources are blended with their neighbors; accordingly, the unWISE analysis simultaneously fits thousands of sources to obtain accurate photometry. Our new catalog detects sources roughly 0.7mag fainter than the AllWISE catalog at 5{sigma}, and more accurately models millions of faint sources in the Galactic plane, enabling a wealth of Galactic and extragalactic science. In particular, relative to AllWISE, unWISE doubles the number of galaxies detected between redshifts 0 and 1 and triples the number between redshifts 1 and 2, cataloging more than half a billion galaxies over the whole sky.