We have investigated the electronic structure of excitons in InP quantum dots in GaInP. The exciton is theoretically expected to have four states. Two of the states are allowed to optically decay to the ground (vacuum) state in the dipole approximation. We see these two lines in photoluminescence (PL) experiments and find that the splitting between the lines (the fine structure splitting) is 150(± 30) µeV. The lines were perpendicularly polarized. We verified that the lines arise from neutral excitons by using correlation spectroscopy. The theoretical calculations show that the polarization of the emission lines are along and perpendicular to the major axis of elongated dots. The fine structure splitting depends on the degree of elongation of the dots and is close to zero for dots of cylindrical symmetry, despite the influence of the piezoelectric polarization, which is included in the calculation.