Ultrafast electron diffraction has been employed for the study of structural dynamics at surfaces in the time domain. Experiments were performed in a pump-probe setup with femtosecond-laser excitation and subsequent probing through diffraction of a femtosecond electron pulse at a temporal resolution of 350 fs. The system of interest is one atomic layer of indium atoms on a Si(111) surface. Through self-assembly, indium atomic wires form and exhibit a Peierls-like, insulator-to-metal phase transition that can be driven nonthermally through a femtosecond laser pulse. The transient intensity of the diffraction spots indicates the lifting of the Peierls transition and melting of a charge-density wave in only 700 fs, heating of the surface in 6 ps, and formation of a metastable and supercooled phase, which exists for nanoseconds.