The design of a parallel implementation of multilevel recursive spectral bisection on the Cray T3D is described. The code is intended to be fast enough to enable dynamic repartitioning of adaptive meshes and to partition meshes that are too large for workstations. Two innovations in the implementation are recursive asynchronous task teams and a parallel version of the multilevel accelerator. A performance improvement of a factor of 140 over the best available serial implementation is demonstrated.