The ability to use mechanical strain to steer chemical reactions creates completely new opportunities for solution- and solid-phase synthesis of functional molecules and materials. However, this strategy is not readily applied in the bottom-up on-surface synthesis of well-defined nanostructures. We report an internal strain-induced skeletal rearrangement of one-dimensional (1D) metal-organic chains (MOCs) via a concurrent atom shift and bond cleavage on Cu(111) at room temperature. The process involves Cu-catalyzed debromination of organic monomers to generate 1,5-dimethylnaphthalene diradicals that coordinate to Cu adatoms, forming MOCs with both homochiral and heterochiral naphthalene backbone arrangements. Bond-resolved non-contact atomic force microscopy imaging combined with density functional theory calculations showed that the relief of substrate-induced internal strain drives the skeletal rearrangement of MOCs via 1,3-H shifts and shift of Cu adatoms that enable migration of the monomer backbone toward an energetically favorable registry with the Cu(111) substrate. Our findings on this strain-induced structural rearrangement in 1D systems will enrich the toolbox for on-surface synthesis of novel functional materials and quantum nanostructures.