Solutions of wormlike tetradecyltrimethylammonium salicylate (TTASal) micelles in the presence of electrolyte are examined in a uniaxial elongational flow field. We show that, in contrast with their shear thinning behavior, these solutions elongationally thicken in a similar manner to polymer solutions. The dynamic nature of these micelles affects their flow behavior, causing micelle growth in the elongational field up to a critical rate of strain, above which a reversible thinning occurs. Flow visualization experiments also indicate the formation of a nematic phase under elongation, and this is discussed in terms of current models for micelle dynamics in external fields.