Stable p-type doping of ZnO has been a major technical barrier for the application of ZnO in optoelectronic devices. While p-type conductivity for nitrogen-doped ZnO has been repeatedly reported, its origin remains mysterious. Here, using first-principles calculation, we predict that an ammonia molecule could counterintuitively assume a Zn site and form a substitutional defect, (NH₃)_Zn. By comparing with other molecular dopants (N₂ and NO) on the Zn site and N on the O site (N_O), we found that (NH₃)_Zn is thermodynamically the most stable defect under O-rich conditions. The stability is attributed to the formation of a strong dative bond of the ammonia molecule with a neighbouring O atom. The (NH₃)_Zn defect is neutral regardless of the Fermi level of the system, but it can capture a H donor forming (NH₄)_Zn, which becomes an acceptor. Experimental evidence for the existence of this Zn-site N acceptor is provided based on a comparison of calculated and measured N 1s X-ray photoelectron spectra. Accurately calculating the (0/−) transition level for this and other N-based acceptors has been hindered by the theoretical method used. Experimental studies are called for to clarify its (0/−) transition level.