Magnetization measurements of well-characterized monodisperse Pt clusters consisting of 13+/-2 atoms in a zeolite confirm the predicted extraordinary magnetic polarization with up to 8 unpaired electrons on a cluster, corresponding to a magnetic moment of 0.65(5) microB per atom. The effect is partly quenched by hydrogen chemisorption. The study provides insight into the electronic structure of the cluster and is fundamental for an understanding of how magnetism develops in small clusters.