The goal of this study was to explore the rate-dependent behavior of the stretch-induced polydomain-monodomain (PM) transition of a liquid crystal elastomer (LCE). The main-chain LCE was synthesized and then cross-linked in the nematic polydomain state. The PM transition caused a soft-elastic behavior, which was measured using uniaxial tensile tests at multiple strain rates and temperatures. The main finding was that we were able to apply the temperature-dependent shift factor determined for the small strain behavior and in the frequency domain to create master curves for the large-strain response in the strain rate domain. The soft elasticity phenomenon was absent from the stress-strain curve at equilibrium. The results also suggest that the relaxation mechanisms of the network, and not of the mesogen orientation, dominate the rate-dependent behavior. Finally, we observed a relatively slow recovery behavior, suggesting the presence of an additional slow relaxation mechanism.