Upgraded network technology presents an advanced technological platform for telecare medicine information systems (TMIS) for patients. However, TMIS generally suffers various attacks since the information being shared through the insecure channel. Recently, many authentication techniques have been proposed relying on the chaotic map. However, many of these designs are not secure against the known attacks. In spite of the fact that some of the constructions attain low computation overhead, they cannot establish an anonymous communication and many of them fail to ensure forward secrecy. In this work, our aim is to present authentication and key agreement protocol for TMIS utilizing a chaotic map to achieve both security and efficiency. The underlying security assumptions are chaotic theory assumptions. This scheme supports forward secrecy and a secure session is established with just two messages of exchange. Moreover, we present a comparative analysis of related authentication techniques.