One-dimensional wires are known to be inherently unstable at finite temperature. Here, we show that long-range order of atomic Au double chains adsorbed on a Si(553) surface is not only stabilized by interaction with the substrate, but spontaneous self-healing of structural defects is actually enforced by the adsorption of atomic species such as Au or H. This is true even for random adsorbate distribution. Combining atomistic models within density functional theory with low energy electron diffraction and high-resolution electron energy loss spectroscopy, we demonstrate that this apparently counterintuitive behavior is mainly caused by adsorption-induced band filling of modified surface bands, i.e., by the strong electronic correlation throughout the whole terrace. Although adsorption preferably occurs at the step edge, it enhances the dimerization and the stiffness of the Au dimers. Thus, the intertwinement of quasi-1D properties with delocalized 2D effects enforces the atomic wire order.