Whenever a nanosystem such as an adatom, a cluster or a nanowire spontaneously magnetizes, a crucial parameter is its magnetic anisotropy, the intrinsic preference of magnetization to lie along an easy axis. Anisotropy is important in nanosystems because it helps reduce the magnitude of thermal (superparamagnetic) fluctuations, it can modify the flow of current, and it can induce new phenomena, such as the quantum tunnelling of magnetization. We discuss here, on the basis of density functional calculations, the novel and unconventional feature of colossal magnetic anisotropy -the strict impossibility of magnetization to rotate from the parallel to the orthogonal direction- which, owing to a quantum mechanical selection rule, the recently predicted Pt nanowire magnetism should exhibit. Model calculations suggest that the colossal magnetic anisotropy of a Pt chain should persist after weak adsorption on an inert substrate or surface step.