Clustered sensor networks have been shown to increase system throughput, decrease system delay, and save energy. While those with rotating cluster heads, such as LEACH, have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we show how random key predistribution, widely studied in the context of flat networks, can be used to secure communication in hierarchical (cluster-based) protocols such as LEACH. To our knowledge, it is the first work that investigates random key predistribution as applied to hierarchical WSNs.