We present the third open gravitational-wave catalog (3-OGC) of compact-binary coalescences, based on the analysis of the public LIGO and Virgo data from 2015 through 2019 (O1, O2, O3a). Our updated catalog includes a population of 57 observations, including 4 binary black hole mergers that had not been previously reported. This consists of 55 binary black hole mergers and the 2 binary neutron star mergers, GW170817 and GW190425. We find no additional significant binary neutron star or neutron star-black hole merger events. The most confident new detection is the binary black hole merger GW190925_232845, which was observed by the LIGO-Hanford and Virgo observatories with P astro > 0.99 its primary and secondary component masses are 20.2-2.5+3.9 M O ˙ and 15.6-2.6+2.1,M o ˙, respectively. We estimate the parameters of all binary black hole events using an up-to-date waveform model that includes both subdominant harmonics and precession effects. To enable deep follow up as our understanding of the underlying populations evolves, we make available our comprehensive catalog of events, including the subthreshold population of candidates, and the posterior samples of our source parameter estimates.