Using scanning tunneling microscopy (STM) at low temperatures, we have studied the transition between the c(4X2) and (2X1) phases of Si(100). The phase transition is resulting from the stabilization and ordering of asymmetric dimers on reconstructed Si(100) at low temperatures. The occurrence of asymmetric dimers already at room temperature in previous STM results has so far been. associated with defect structures, which were believed to produce a local buckling in an arrangement of symmetric dimers. By cooling Si(100) we observe growth of c(4X2) domains which, below 200 K, cover the entire surface. The phase transition can be explained by freezing in of the vibration of asymmetric dimers, which is present on defect-free parts of the surface at room temperature.