We present the first results from a new carbon monoxide (CO) survey of the southern Galactic plane being conducted with the Mopra radio telescope in Australia. The 12CO, 13CO and C18O J=1-0 lines are being mapped over the l = 305-345 deg, b = +/- 0.5 deg portion of the 4th quadrant of the Galaxy, at 35 spatial and 0.1 km/s spectral resolution. The survey is being undertaken with two principal science objectives: (i) to determine where and how molecular clouds are forming in the Galaxy and (ii) to probe the connection between molecular clouds and the missing gas inferred from gamma-ray observations. We describe the motivation for the survey, the instrumentation and observing techniques being applied, and the data reduction and analysis methodology. In this paper we present the data from the first degree surveyed, l = 323-324 deg, b = +/- 0.5 deg. We compare the data to the previous CO survey of this region and present metrics quantifying the performance being achieved; the rms sensitivity per 0.1 km/s velocity channel is ~1.5K for 12CO and ~0.7K for the other lines. We also present some results from the region surveyed, including line fluxes, column densities, molecular masses, 12CO/13CO line ratios and 12CO optical depths. We also examine how these quantities vary as a function of distance from the Sun when averaged over the 1 square degree survey area. Approximately 2 x 10E6 MSun of molecular gas is found along the G323 sightline, with an average H2 number density of nH2 ~ 1 cm-3 within the Solar circle. The CO data cubes will be made publicly available as they are published.
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