RFID technology shall increase security, e.g. by helping to prevent counterfeiting. But the technology also causes privacy issues. In this paper, after highlighting goals and problems, an approach called "triggered hash chains" is proposed to address the problems. The approach combines concepts of two very different, widely known RFID protocols, i.e. the "hash-based ID variation" approach and the "Hash chain" approach. The resulting proposal joins the advantages of both protocols. The approach is evaluated using a variety of criteria that are relevant in practice.