Wireless Sensor Networks (WSNs) are playing a vital role in an ever-growing number of applications ranging from environmental surveillance over medical monitoring to home automation. Since WSNs are often deployed in unattended or even hostile environments, they can be subject to various malicious attacks, including the manipulation and capture of nodes. The establishment of a shared secret key between two or more individual nodes is one of the most important security services needed to guarantee the proper functioning of a sensor network. Despite some recent advances in this field, the efficient implementation of cryptographic key establishment for WSNs remains a challenge due to the resource constraints of small sensor nodes such as the MICAz mote. In this paper we present a lightweight implementation of the elliptic curve Diffie-Hellman (ECDH) key exchange for ZigBee-compliant sensor nodes equipped with an ATmega128 processor running the TinyOS operating system. Our implementation uses a 192-bit prime field specified by the NIST as underlying algebraic structure and requires only $5.20 \cdot 10^6$ clock cycles to compute a scalar multiplication if the base point is fixed and known a priori. A scalar multiplication using a random base point takes about $12.33 \cdot 10^6$ cycles. Our results show that a full ECDH key exchange between two MICAz motes consumes an energy of 57.33 mJ (including radio communication), which is significantly better than most previously reported ECDH implementations on comparable platforms.