Photofragmentation of the protonated water dimer H+(H2O)_{2}, a fundamental system both in aqueous solutions and gas-phase water clusters, has been studied at 13.8 nm using the Free Electron Laser FLASH in Hamburg. In a crossed-beam experiment using time-resolved, single-molecule fragment imaging, the two-body breakup into H2O++H3O+ was found as a prominent fragmentation channel with a kinetic energy release of up to 10 eV. This channel was observed with at least a similar yield as events with stronger fragmentation, producing protons together with neutral fragments and showing an absolute cross section of (0.5 ± 0.2) × 10(-18) cm2.