Magnetic moments and the magnetic anisotropy energy (MAE) are calculated for Co chains on a stepped Cu(111) surface in a fully relaxed geometry. The Korringa-Kohn-ostoker Green's function method is used to determine parameters of N-body interatomic potentials and to fit the semi-empirical tightbinding electronic Hamiltonian. The strain relief at steps and in the Co chains is demonstrated to have a profound effect on the morphology of the substrate. Atomic relaxations are shown to decrease the magnetic moments and the MAE. The MAE and orbital moments are found to exhibit an oscillatory behavior with increasing size of the chains.