The Great Nebula in Carina provides an exceptional view into the violent massive star formation and feedback that typifies giant HII regions and starburst galaxies. We have mapped the Carina star-forming complex in X-rays, using archival Chandra data and a mosaic of 20 new 60ks pointings using the Chandra X-ray Observatory's Advanced CCD Imaging Spectrometer, as a testbed for understanding recent and ongoing star formation and to probe Carina's regions of bright diffuse X-ray emission. This study has yielded a catalog of properties of >14,000 X-ray point sources; >9800 of them have multiwavelength counterparts. Using Chandra's unsurpassed X-ray spatial resolution, we have separated these point sources from the extensive, spatially-complex diffuse emission that pervades the region; X-ray properties of this diffuse emission suggest that it traces feedback from Carina's massive stars. In this introductory paper, we motivate the survey design, describe the Chandra observations, and present some simple results, providing a foundation for the 15 papers that follow in this Special Issue and that present detailed catalogs, methods, and science results.Comment: Accepted for the ApJS Special Issue on the Chandra Carina Complex Project (CCCP), scheduled for publication in May 2011. All 16 CCCP Special Issue papers are available at http://cochise.astro.psu.edu/Carina_public/special_issue.html through 2011 at least. 43 pages; 18 figure
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