We report a study of the luminescence due to Hg in ZnO, concentrating on the main zero phonon line (ZPL) at 3.2766(1) eV and its associated phonon sidebands. For a sample implanted with radioactive 192Hg, the ZPL intensity, normalised to that of shallow bound exciton emission, is observed to decrease with an equivalent half-life of 4.5(1) h, very close to the 4.85(20) h half-life of 192Hg. ZnO implanted with stable Hg impurities produces the same luminescence spectrum. Temperature dependent measurements confirm that the zero phonon line is a thermalizing doublet involving one allowed and one largely forbidden transition from excited states separated by 0.91(1)meV to a common ground state. Uniaxial stress measurements show that the allowed transition takes place from an orbitally degenerate excited state to a non-degenerate ground state in a centre of trigonal (C3v) symmetry while the magneto-optical properties are characteristic of electron-hole pair recombination at an isoelectronic defect. The doublet luminescence is assigned to bound exciton recombination involving exchange-split gamma5 and gamma1,2 excited states (using C6v symmetry labels; gamma3 and gamma1,2 using C3v labels) at isoelectronic Hg impurities substituting for Zn in the crystal. The electron and hole g values deduced from the magneto-optical data indicate that this Hg impurity centre in ZnO is hole-attractive.