Several new emissions due to excitons bound at neutral complexes are observed in GaP upon diffusion with Cu and subsequently with Li. Here we report work on the most shallow of these centers, with lowest electronic transition at 2.306 eV. This center, which we denote as (Cu-Li)I, is studied by means of photoluminescence, photoluminescence excitation, and magneto-optical work. The luminescence spectrum exhibits a pair of electronic lines of singlet-triplet multiplicity as revealed by magnetic field measurements. This configuration has been shown to be characteristic of certain defect complexes in cubic semiconductors. These centers are dominated by a compressive local strain field combined with a hole-attractive central cell of the neutral complex. Optically detected magnetic-resonance measurements determine the symmetry of the (Cu-Li)I complex as orthorhombic with the z axis 111-oriented. The phonon sideband of the luminescence is richly structured and the well-resolved phonon spectra contain two true local modes and a gap mode in addition to the usual zone-boundary modes of GaP. The local modes show substantial energy shift when replacing Li7 with Li6, thus proving the presence of Li in the complex. No new local modes appear after mixed isotope doping indicating the presence of only one Li atom. Lifetime measurements reveal a very long decay time for the triplet line of =1 ms, whereas the singlet has a more allowed character with =20 s. The long radiative lifetime is consistent with no free spin in the final state of the transition. This agrees with the observed thermalization between the magnetic subcomponents of the triplet, proving that the splitting in magnetic field occurs in the initial state of the transition. The compiled data suggest an orthorhombic 111-oriented complex consisting of CuGa in combination with a pair of interstitial atoms, of which one is known to be Li, as the identity of the (Cu-Li)I center.