The Mopra CO survey of the Southern Galactic Plane is being conducted with the Mopra millimetre-wave telescope in Coonabarabran, New South Wales, Australia. The survey is designed to map the distribution and dynamics of the carbon monoxide molecule (CO) along a 120 degree sector of the Galactic Plane, from l=250-370deg. The principal scientific motivations are to study how molecular clouds are formed in space, and to examine the nature of TeV gamma-ray sources observed with H.E.S.S and the forthcoming Cherenkov Telescope Array. Data Release 3 contains observations of fifty square degrees of the Mopra carbon monoxide (CO) survey of the Southern Galactic Plane, covering Galactic longitudes l = 300-350deg and latitudes |b| %3C= 0.5deg. These data have been taken at 0.6arcminute spatial resolution and 0.1kms-1 spectral resolution, providing an unprecedented view of the molecular clouds and gas of the Southern Galactic Plane in the 109-115 GHz J = 1-0 transitions of 12CO, 13CO, C18O and C17O.Original acknowledgement for data: The Mopra CO data were obtained using the Mopra radio telescope, a part of the Australia Telescope National Facility. The University of New South Wales (UNSW) digital filter bank (the UNSW-MOPS) used for the observations with Mopra was provided with support from the Australian Research Council (ARC), UNSW, Sydney and Monash Universities, as well as the CSIRO.