We present a 1.42 square degree mosaic of diffuse X-ray emission in the Great Nebula in Carina from the Chandra X-ray Observatory Advanced CCD Imaging Spectrometer camera. After removing >14,000 X-ray point sources from the field, we smooth the remaining unresolved emission, tessellate it into segments of similar apparent surface brightness, and perform X-ray spectral fitting on those tessellates to infer the intrinsic properties of the X-ray-emitting plasma. By modeling faint resolved point sources, we estimate the contribution to the extended X-ray emission from unresolved point sources and show that the vast majority of Carina's unresolved X-ray emission is truly diffuse. Line-like correlated residuals in the X-ray spectral fits suggest that substantial X-ray emission is generated by charge exchange at the interfaces between Carina's hot, rarefied plasma and its many cold neutral pillars, ridges, and clumps. ; 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. 32 pages, 14 figures