We present a measurement of the systemic proper motion of the Large Magellanic Cloud ( LMC ) from astrometry with the High Resolution Camera ( HRC ) of the Advanced Camera for Surveys ( ACS ) on the Hubble Space Telescope ( HST ) . We observed LMC fields centered on 21 background QSOs that were discovered from their optical variability in the MACHO database . The QSOs are distributed homogeneously behind the central few degrees of the LMC . With 2 epochs of HRC data and a \sim 2 year baseline we determine the proper motion of the LMC to better than 5 % accuracy : \mu _ { W } = -2.03 \pm 0.08 { mas yr ^ { -1 } } , \mu _ { N } = 0.44 \pm 0.05 { mas yr ^ { % -1 } } . This is the most accurate proper motion measurement for any Milky Way satellite thus far . When combined with HI data from the Magellanic Stream this should provide new constraints on both the mass distribution of the Galactic Halo and models of the Stream .