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We explore the possibility that the observed population of Galactic hypervelocity stars (HVSs) originate as runaway stars from the Large Magellanic Cloud (LMC). Pairing a binary evolution code with an N-body simulation of the interaction of the LMC with the Milky Way, we predict the spatial distribution and kinematics of an LMC runaway population. We find that runaway stars from the LMC can contribute Galactic HVSs at a rate of three every million years. This is composed of stars at different points of stellar evolution, ranging from the main-sequence to those at the tip of the asymptotic giant branch. We find that the known B-type HVSs have kinematics which are consistent with an LMC origin. There is an additional population of hypervelocity white dwarfs whose progenitors were massive runaway stars. Runaways which are even more massive will themselves go supernova, producing a remnant whose velocity will be modulated by a supernova kick. This latter scenario has some exotic consequences, such as pulsars and supernovae far from star-forming regions, and a small rate of microlensing from compact sources around the halo of the LMC.