A one-dimensional monatomic chain under tensile stress has been studied by molecular dynamics. The aim is to determine the lifetime to chain breakage and to ascertain whether this event can be described by simple statistical reaction rate theory. Chains of 2-20 atoms have been simulated. A simple transition state theory, equivalent to a nucleation theory for one-dimensional fluids, gives the main features of the decay rate coefficient as a function of the applied stress. For finite chain lengths an anharmonic RRKM theory provides a more accurate rate coefficient, but chain healing (reversible decay) in the simulated motion causes a significant deviation, particularly at high chain energy. The simulation is extended to chain arrays which show greatly increased nonstatistical effects.