By using quantitative low energy electron diffraction, we have studied the temperature-driven phase transition of Pb chains grown on Si(557) substrates at a surface concentration of 1.3 ML. This concentration, which is still below one physical monolayer, exhibits a unique switching of electrical conductance from one dimensional to two dimensional above 78 K, which is coupled to this phase transition, and was investigated for this reason. Annealing to 640 K causes a concentration-driven refacetting of the whole surface into large (223) facets at low temperatures, while along the chains a so-called (1,5) linear phase is formed, causing a tenfold periodicity. At Tc=78 K, we analyze a temperature-driven order-order transition along the [¯1¯12] direction in detail, which again turns out to be a refacetting transition. The two-dimensional character of this transition was seen by corresponding structural changes along the [1¯10] direction as well. Refacetting causes a change in periodicity and destroys the conditions of Fermi nesting necessary for one-dimensional conductance. © 2008 The American Physical Society.