We present an analysis of the stellar kinematics of the Large Magellanic Cloud based on ~5900 new and existing velocities of massive red supergiants, oxygen-rich and carbon-rich AGB stars, and other giants. After correcting the line-of-sight velocities for the LMCs space motion and accounting for asymmetric drift in the AGB population, we derive a rotation curve that is consistent with all of the tracers used, as well as that of published HI data. The amplitude of the rotation curve is v_0=87+/-5 km s^-1 beyond a radius R_0=2.4+/-0.1 kpc, and has a position angle of the kinematic line of nodes of theta=142 degrees +/-5 degrees. By examining the outliers from our fits, we identify a population of 376 stars, or >~5% of our sample, that have line-of-sight velocities that apparently oppose the sense of rotation of the LMC disk. We find that these kinematically distinct stars are either counter-rotating in a plane closely aligned with the LMC disk, or rotating in the same sense as the LMC disk, but in a plane that is inclined by 54 degrees +/- 2 degrees to the LMC. Their kinematics clearly link them to two known HI arms, which have previously been interpreted as being pulled out from the LMC. We measure metallicities from the Ca triplet lines of ~1000 LMC field stars and 30 stars in the kinematically distinct population. For the LMC field, we find a median [Fe/H]=-0.56 +/- 0.02 with dispersion of 0.5 dex, while for the kinematically distinct stars the median [Fe/H] is -1.25 +/- 0.13 with a dispersion of 0.7 dex. The metallicity differences provide strong evidence that the kinematically distinct population originated in the SMC. This interpretation has the consequence that the HI arms kinematically associated with the stars are likely falling into the LMC, instead of being pulled out.
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