We present evidence for a Spitzer-selected luminous infrared galaxy (LIRG) behind the Bullet Cluster. The galaxy, originally identified in IRAC photometry as a multiply imaged source, has a spectral energy distribution consistent with a highly extincted (A_V~3.3), strongly star-forming galaxy at z=2.7. Using our strong gravitational lensing model presented in Bradac et al. (2006), we find that the magnifications are 10 to 50 for the three images of the galaxy. The implied infrared luminosity is consistent with the galaxy being a LIRG, with a stellar mass of M_*~2e11 M_Sun and a star formation rate of ~90 M_Sun/yr. With lensed fluxes at 24 microns of 0.58 mJy and 0.39 mJy in the two brightest images, this galaxy presents a unique opportunity for detailed study of an obscured starburst with star fomation rate comparable to that of L* galaxies at z>2.