The Pb/Si(557) system exhibits a strong anisotropy in conductance below 78 K, with the evolution of a characteristic chain structure. Here we show, using angle-resolved photoemission, that chain ordering results in complete Fermi-like nesting in the direction normal to the chains; in addition, the domain structure along the chains forms split-off valence bands with mesoscopic Fermi wavelengths which induce the 1D conductance without further instabilities at low temperatures.