One-dimensional Co atomic wires grown on Pt(997) have been investigated by x-ray magnetic circular dichroism. Strong changes of the magnetic properties are observed as the system evolves from 1D- to 2D-like. The easy axis of magnetization, the magnetic anisotropy energy, and the coercive field oscillate as a function of the transverse width of the wires, in agreement with theoretical predictions for 1D metal systems.