The zCOSMOS redshift survey used 600h on the VIMOS spectrograph spread over five observing seasons (2005-2009) to obtain spectra of about 20,000 galaxies selected to have Iab < 22.5 across the full 1.7 deg2 of the COSMOS field. This part, "zCOSMOS-bright", was designed to yield a high and fairly uniform sampling rate (about 70%), with a high success rate in measuring redshifts (approaching 100% at 0.5 < z < 0.8), and with sufficient velocity accuracy (about 100 km/s) to efficiently map the environments of galaxies down to the scale of galaxy groups out to redshifts z ~ 1.