The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.