With the development of Internet, patients could enjoy health-care delivery services through telecare medicine information systems (TMIS) in their home. To control the access to remote medical servers' resources, many authentication schemes using smart cards have been proposed. However, the performance of these schemes is not satisfactory since modular exponential operations are used in these schemes. In the paper, we propose a chaotic map-based authentication scheme for telecare medicine information systems. The security and performance analysis shows our scheme is more suitable for TMIS.