We present an arc-like continuum X and a mapping f : X --> X with the following properties: The set of recurrent points of f is dense in X
f has no periodic points other than fixed points
and the topological entropy of f is positive. This example allows us to answer one question due to J.J. Charatonik and another question due to M. Barge. (C) 2002 Elsevier Science B.V. All rights reserved.