We report spectroscopic confirmation and high-resolution infrared imaging of a z = 2.79 triply imaged galaxy behind the Bullet Cluster. This source, a Spitzer-selected luminous infrared galaxy, is confirmed via polycyclic aromatic hydrocarbon (PAH) features using the Spitzer Infrared Spectrograph (IRS) and resolved with Hubble Space Telescope Wide Field Camera 3 imaging. In this galaxy, which with a stellar mass M{sub *} {approx} 4 x 10{sup 9} M{sub sun} is one of the two least massive ones studied with IRS at z>2, we also detect H{sub 2} S(4) and H{sub 2} S(5) pure rotational lines (at 3.1{sigma} and 2.1{sigma})-the first detection of these molecular hydrogen lines in a high-redshift galaxy. From the molecular hydrogen lines we infer an excitation temperature T = 377{sup +68}{sub -84} K. The detection of these lines indicates that the warm molecular gas mass is 6{sup +36}{sub -4}% of the stellar mass and implies the likely existence of a substantial reservoir of cold molecular gas in the galaxy. Future spectral observations at longer wavelengths with facilities such as the Herschel Space Observatory, the Large Millimeter Telescope, and the Atacama Pathfinder Experiment thus hold the promise of precisely determining the total molecular gas mass. Given the redshift, and using refined astrometric positions from the high-resolution imaging, we also update the magnification estimate and derived fundamental physical properties of this system. The previously published values for L{sub IR}, star formation rate, and dust temperature are confirmed modulo the revised magnification; however, we find that PAH emission is roughly a factor of 5 stronger than would be predicted by the relations between L{sub IR} and L{sub PAH} reported for SMGs and starbursts in Pope et al.