We have investigated Pd nanowires theoretically, and found that, unlike either metallic or free atomic Pd, they exhibit Hund.s rule magnetism. In long, monostrand nanowires, we find a spin moment of 0.7μ_B per atom, whereas for short, monostrand nanowires between bulk leads, the predicted moment is about 0.3μ_B per nanowire atom. In contrast, a coaxial (6,1) nanowire was found to be nonmagnetic. The origin of the nanowire magnetism is analyzed.