In LiNbO₃ single crystals doped with 8 mol% Mg and gamma irradiated at 77 K a new trapped-hole defect has been detected. The new defect is characterized by an anisotropic ESR spectrum with a nearly isotropic, partly resolved hyperfine structure due to a single Nb nucleus. The principal g-values are g₁=2.029+or-0.010, g₂=2.049+or-0.010 and g₃=2.006+or-0.010, the Nb hyperfine constant is A=1.5+or-0.2 mT. The new spectrum is attributed to a hole localized on an oxygen ion and stabilized by a substitutional Mg²⁺ ion on the nearest-neighbour Nb site, with an appreciable spin density on the other close Nb neighbour of the oxygen. The new defect, called the O^-(Mg) centre, appears in these crystals together with OH^2- trapped electron centres reported recently. The O^-(Mg) centres can be produced in larger concentrations if the crystal contains, in addition to an over-threshold (6-8 mol%) amount of Mg, also the Fe dopant. This is attributed to the electron-trapping capabilities of Fe³⁺ centres. The O^-(Mg) centre decays in the temperature range 170-230 K, i.e. is more stable than the O^- centre reported previously for undoped or weakly Mg-doped LiNbO₃.