I will discuss an analysis of the stellar kinematics of the Large Magellanic Cloud based on several thousand spectra, obtained with Hydra-CTIO, of massive red supergiants, oxygen-rich and carbon-rich AGB stars, and other giants. We have used the stellar velocities to measure the rotation curve of the LMC, which we find to have an amplitude of 87 ± 5 km/s, a value that is in agreement with all of the available kinematic tracers. Our data also reveal a population of outliers, comprising ~5% of the sample, that have line-of-sight velocities that apparently oppose the sense of rotation of the LMC disk. I will show that these outliers likely represent stars that were accreted by the LMC from the SMC. The accretion of these SMC stars and gas by the LMC may have been the trigger for the intense star formation that we now see in 30 Doradus, the most active star formation complex in the nearby Universe. I will also describe our related DECam observing program, which aims to map Magellanic Cloud stellar populations out to large radius from the parent galaxies.