We used ultrafast electron diffraction and density-functional theory calculations to gain insight into the charge density wave (CDW) formation on In/Si(111). Weak excitation by a femtosecond-laser pulse results in the melting of the CDW. The immediate freezing is hindered by a barrier for the motion of atoms during the phase transition: The melted CDW constitutes a long-lived, supercooled phase and is strong evidence for a first-order transition. The freezing into the CDW is triggered by preexisting adsorbates. Starting at these condensation nuclei, the CDW expands one dimensionally on the In/Si(111) surface, with a constant velocity of more than 80  m/s.