We show that the nonlinear a-model in an asymptotically AdS(3) space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear a-model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear a-model fields and changes the space-time metric, and it can be used to map the extremal BTZ black hole to infinitely many hairy black hole solutions. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.