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Clustering is a useful mechanism in wireless sensor networks that helps to cope with scalability problems and, if combined with in-network data aggregation, may increase the energy efficiency of the network. At the same time, by assigning a special role to the cluster head nodes, clustering makes the network more vulnerable to attacks. In particular, disabling a cluster head by physical destruction or jamming may render the entire cluster inoperable temporarily until the problem is detected and a new cluster head is elected. Hence, the cluster head nodes may be attractive targets of attacks, and one would like to make it difficult for an adversary to identify them. The adversary can try to identify the cluster head nodes in various ways, including the observation of the cluster head election process itself and the analysis of the traffic patterns after the termination of the cluster head election. In this paper, we focus on the former problem, which we call the private cluster head election problem. This problem has been neglected so far, and as a consequence, existing cluster head election protocols leak too much information making the identification of the elected cluster head nodes easy even for a passive external observer. We propose the first private cluster head election protocol for wireless sensor networks that is designed to hide the identity of the elected cluster head nodes from an adversary that can observe the execution of the protocol.