We have investigated the adsorption of O₂ on Au_n clusters (n = 1–6) supported by an ultra thin (3ML)MgO(001) film on Mo metal via density functional theory calculations. On thin films, these small clusters have chain like structures and their electronic states resemble 1D quantum well states. The Au_1–3 are charged by one electron whereas the larger Au_4–6 get two electrons from the substrate. This is confirmed both by the symmetries of the HOMO and LUMO states of the clusters and the Bader charge analysis. In contrast to the O₂ adsorption on gas-phase clusters, the adsorption energy of O₂ molecule does not show pronounced oscillations as a function of cluster size. The O₂ is activated (i.e. the O–O bond is elongated and the molecule is charged) in contact with all the cluster sizes. O₂ activation and strong binding is also observed on bare MgO/Mo, whereas the molecule interacts only weakly with bulk MgO. The activation of O₂ is mainly due to charge transferred from the support. The relevance of these results for catalytic activity of small thin-film-supported clusters is discussed.