The origin of a triplet (S = 1) optically detected magnetic-resonance (ODMR) spectrum observed in the luminescence of GaP:O has been the subject of recent controversy. Originally identified with the negative-charge state of a substitutional oxygen impurity, more recent suggestions have interpreted a resolved I = 3/2 hyperfine interaction in the ODMR to indicate an interstitial-gallium-related defect. We report here optical detection of electron-nuclear double resonance (ODENDOR) of the central I = 3/2 nucleus and confirm unambiguously that it is gallium. Its magnetic hyperfine and nuclear quadrupole interactions are determined and an improved analysis of the electron spin Hamiltonian is presented. A possible model for the defect is suggested: a <100>-oriented Ga(i)V(Ga) pair stabilized by the presence of one or two nearby substitutional oxygen donors. The ODENDOR spectrum arises from the M = o state, causing unusual magnetic-field and orientation effects. The origin of these effects is described and the procedure of analysis to extract the hyperfine parameters is outlined.