We present Chandra X-ray Observatory monitoring observations of the recent accretion outburst displayed by the pre-main sequence (pre-MS) star V1647 Ori. The X-ray observations were obtained over a period beginning prior to outburst onset in late 2003 and continuing through its apparent cessation in late 2005, and demonstrate that the mean flux of the spatially coincident X-ray source closely tracked the near-infrared luminosity of V1647 Ori throughout its eruption. We find negligible likelihood that the correspondence between X-ray and infrared light curves over this period was the result of multiple X-ray flares unrelated to the accretion burst. The recent Chandra data confirm that the X-ray spectrum of V1647 Ori hardened during outburst, relative both to its pre-outburst state and to the X-ray spectra of nearby pre-MS stars in the L1630 cloud. We conclude that the observed changes in the X-ray emission from V1647 Ori over the course of its 2003-2005 eruption were generated by a sudden increase and subsequent decline in its accretion rate. These results for V1647 Ori indicate that the flux of hard X-ray emission from erupting low-mass, pre-MS stars, and the duration and intensity of such eruptions, reflect the degree to which star-disk magnetic fields are reorganized before and during major accretion events.