The radii of gyration of wormlike "living polymer" micelles of tetradecyltrimethylammonium bromide/salicylate have been measured in an elongational field at various elongation rates. The radius of gyration in the now direction first increases, indicating alignment with the field, reaching a maximum at a critical elongation rate before falling. This decrease is taken as evidence for micelle scission at high velocity gradients. The microscopic structural measurements are consistent with inferences drawn from rheological measurements on similar systems.