Absolute single photoionization cross section measurements for Br3+ ions are reported in the photon energy range 44.79-59.54 eV at a photon energy resolution of 21 ±3 meV. Measurements were performed at the Advanced Light Source at Lawrence Berkeley National Laboratory using the merged-beams technique. Numerous resonance features in the experimental spectrum are assigned and their energies and quantum defect values are tabulated. The cross-section measurements are also compared with Breit-Pauli R-matrix calculations with suitable agreement over the photon energy range investigated. Analysis of the measured spectrum including Rydberg resonance series identifications produced a new emperical determination of the ionizational potential of Br3+ of 46.977 ± 0.050 eV, which is 805 meV lower than the most recently published value of 47.782 eV. This disparity between our determination and the earlier published value is similar to an 843 meV shift in the accepted ionization potential published for iso-electronic Se2+ as part of this same research program.