We have carried out a systematic study of N2O dissociation on a TiO2 (110) surface by means of plane-wave pseudopotential density-functional theory calculations. We have made use of both static and dynamic calculations in order to elucidate N2O decomposition mechanisms. We find that dissociation is not favorable on the stoichiometric surface. On the other hand, the presence of oxygen bridging vacancies make the NO decomposition possible. The role of the defective surface is to provide electrons to the adsorbed molecule. We find two channels for decomposition, depending on whether the molecule is adsorbed with the O or the N end of the molecule on a vacancy. The first case is energetically downhill and proceeds spontaneously, leading to N-2 ejection from the surface and vacancy oxidation. The second case relies on the formation of an intermediate bridging configuration of the adsorbed molecule and is hindered by a small energy barrier. In this case, molecule breaking produces N-2 in the gas phase and leaves oxygen adatoms on the surface. We relate our results to recent experimental findings.