X-irradiation of a single crystal of triphenyliminophosphonium bromide yields an oriented free radical which is identified via its ESR spectrum as the triphenylbromophosphoranyl radical, Ph₃PBr. The g tensor, the magnetic hyperfine tensors of the ³¹P and ⁸¹Br nuclei and the quadrupole coupling tensor of the ⁸¹Br nucleus are reported. The directions of the maximum value of the ³¹P magnetic hyperfine tensor and of the ⁸¹Br magnetic hyperfine tensor are inclined at an angle of 35° thus indicating a structure intermediate between the C_2v structure of PF₄ and the C_3v structure of Ph₃PCl.