One-dimensional chain-like structures consisting of rows of single chromium adatoms have been obtained by annealing a submonolayer chromium film deposited under ultra-high vacuum (UHV) conditions onto a Cr(100) single crystal substrate. The self-organization of the Cr atoms under the influence of the substrate surface potential leads to two kinds of atomic rows orientated in orthogonal directions, thereby reflecting the symmetry of the Cr(100) surface potential. The formation of these atomic-scale wires has been monitored in-situ by means of a UHV scanning tunneling microscope (STM).