ContextWe analyze these HIFI data with non-local thermodynamic equilibrium radiative transfer and PDR chemical models, using newly calculated inelastic collision data for the e-OH + system. Results. Line emission is detected over ∼1 (0.12 pc), tracing the Bar itself as well as a perpendicular feature identified as the southern tip of the Orion Ridge, which borders the Orion Nebula on its western side. The line width of ≈4 km s −1 suggests an origin of the OH + emission close to the PDR surface, at a depth of A V ∼ 0.3-0.5 into the cloud where most hydrogen is in atomic form. Steadystate collisional and radiative excitation models for OH + require unrealistically high column densities to match the observed line intensity, indicating that the formation of OH + in the Bar is rapid enough to influence its excitation. Our best-fit OH + column density of ∼1.0 × 10 14 cm −2 is similar to that in previous absorption line studies, while our limits on the ratios of OH + /H 2 O + ( > ∼ 40) and OH + /H 3 O + ( > ∼ 15) are somewhat higher than seen before. Conclusions. The column density of OH + is consistent with estimates from a thermo-chemical model for parameters applicable to the Orion Bar, given the current uncertainties in the local gas pressure and the spectral shape of the ionizing radiation field. The unusually high OH + /H 2 O + and OH + /H 3 O + ratios are probably due to the high UV radiation field and electron density in this object. In the Bar, photodissociation and electron recombination are more effective destroyers of OH + than the reaction with H 2 , which limits the production of H 2 O + . The appearance of the OH + lines in emission is the result of the high density of electrons and H atoms in the Orion Bar, since for these species, inelastic collisions with OH + are faster than reactive ones. In addition, chemical pumping, far-infrared pumping by local dust, and near-UV pumping by Trapezium starlight contribute to the OH + excitation. Similar conditions may apply to extragalactic nuclei where H n O + lines are seen in emission.