Wireless Sensor Networks (WSNs) are characterized by resource constraints and large scalability. Many applications of WSN require secure communication, a crucial component especially in hostile environments. However, the low computational capability and small storage budget within sensors render many popular public-key based cryptographic systems impractical. Symmetric key cryptography, on the other hand, is attractive due to efficiency. Nevertheless, establishing a shared key for communicating parties is a challenging problem. In this paper, we propose and analyze an in-situ PAirwise Key bootstrapping scheme (iPAK) for large-scale WSNs. Our theoretical analysis and simulation study demonstrate that iPAK can achieve high key-sharing probability between neighboring sensors and strong resilience against node capture attacks at the cost of a low storage overhead.