The Census of High- and Medium-mass Protostars (CHaMP) is the first large-scale, unbiased, uniform mapping survey at sub-parsec scale resolution of 90 GHz line emission from massive molecular clumps in the Milky Way. We present the first Mopra (ATNF) maps of the CHaMP survey region (300{deg}>l>280{deg}) in the HCO+ J=1-0 line, which is usually thought to trace gas at densities up to 10^11 m-3. In this paper we introduce the survey and its strategy, describe the observational and data reduction procedures, and give a complete catalogue of moment maps of the HCO+ J=1-0 emission from the ensemble of 301 massive molecular clumps. From these maps we also derive the physical parameters of the clumps, using standard molecular spectral-line analysis techniques. This analysis yields the following range of properties: integrated line intensity 1-30 K km s-1, peak line brightness 1-7 K, linewidth 1-10 km s-1, integrated line luminosity 0.5-200 K km s-1 pc^2, FWHM size 0.2-2.5 pc, mean projected axial ratio 2, optical depth 0.08-2, total surface density 30-3000 M{sun} pc-2, number density 0.2-30 x 10^9 m-3, mass 15-8000 M{sun}, virial parameter 1-55, and total gas pressure 0.3-700 pPa. We find that the CHaMP clumps do not obey a Larson-type size-linewidth relation. Among the clumps, there exists a large population of subthermally excited, weakly-emitting (but easily detectable) dense molecular clumps, confirming the prediction of Narayanan et al. (2008). These weakly-emitting clumps comprise 95% of all massive clumps by number, and 87% of the molecular mass, in this portion of the Galaxy; their properties are distinct from the brighter massive star-forming regions that are more typically studied. If the clumps evolve by slow contraction, the 95% of fainter clumps may represent a long-lived stage of pressure-confined, gravitationally stable massive clump evolution, while the CHaMP ... (abridged)
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