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The Leading Arm (LA) of the Magellanic Stream is a vast debris field of H i clouds connecting the Milky Way and the Magellanic Clouds. It represents an example of active gas accretion onto the Galaxy. Previously, only one chemical abundance measurement had been made in the LA. Here we present chemical abundance measurements using Hubble Space Telescope/Cosmic Origins Spectrograph and Green Bank Telescope spectra of four AGN sightlines passing through the LA and three nearby sightlines that may trace outer fragments of the LA. We find low oxygen abundances, ranging from solar to solar, in the confirmed LA directions, with the lowest values found in the region known as LA III, farthest from the LMC. These abundances are substantially lower than the single previous measurement, S/H = 35 ± 7% solar, but are in agreement with those reported in the SMC filament of the trailing Stream, supporting a common origin in the SMC (not the LMC) for the majority of the LA and trailing Stream. This provides important constraints for models of the formation of the Magellanic System. Finally, two of the three nearby sightlines show high-velocity clouds with H i columns, kinematics, and oxygen abundances consistent with LA membership. This suggests that the LA is larger than traditionally thought, extending at least 20° further to the Galactic northwest. [ABSTRACT FROM AUTHOR]