A Bluetooth ad hoc network can be formed by interconnecting piconets into scatternets. The constraints and properties of Bluetooth scatternets present special challenges in forming an ad hoc network efficiently. We present and analyse a new randomized distributed algorithm for Bluetooth scatternet formation. We prove that our algorithm achieves O(log n) time complexity and O(n) message complexity. We show that: (1) in the scatternet formed by our algorithm, any device is a member of at most two piconets; (2) the number of piconets is close to being minimal.