Density functional calculations and ab initio molecular dynamics simulations are performed to investigate adsorption and dissociation of O-2 molecules on the DI (double icosahedron) Pd19 nanocluster. Exceptionally high activity is found for oxygen bond cleavage over its waist region, with an energy barrier of only 0.06 eV and a reaction time of 0.5 ps. This stems from the availability of valley-like Pd-4 ensembles and the large weights of LUMO and HOMO. Moreover, this cluster is highly stable in reaction conditions up to 500 K, so it can be a good candidate for the development of excellent nanocatalysts.