Density-functional theory is used to explore the Si(553)-Au surface dynamics. Our study (i) reveals a complex two-stage order-disorder phase transition where with rising temperature first the ×3 order along the Si step edges and, subsequently, the ×2 order of the Au chains is lost, (ii) identifies the transient modification of the electron chemical potential during soft Au chain vibrations as instrumental for disorder at the step edge, and (iii) shows that the transition leads to a self-doping of the Si dangling-bond wire at the step edge. The calculations are corroborated by Raman measurements of surface phonon modes and explain previous electron diffraction, scanning tunneling microscopy, and surface transport data.