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The head direction (HD) cell system in the brain of mammals is thought to be part of the neural circuitry supporting their spatial navigation capabilities. In this paper we present a neuromorphic very large scale integration system that models the operation of the HD system. Relying on spiking neurons and attractor dynamics, this system can be used to represent and retain the current estimate of head orientation in the environment and integrate the angular velocity to update this estimate. The presented system is more than a simple integrator and orientation memory; it is a first step towards modeling sophisticated biological navigation systems that use multimodal sensory and motor information to continually realign themselves based on experience.