Sequential multi-constraint graph partitioners have been developed to address the load balancing requirements of multi-phase simulations. The efficient execution of large multi-phase simulations on high performance parallel computers requires that the multi-constraint partitionings are computed in parallel. This paper presents a parallel formulation of a recently developed multi-constraint graph partitioning algorithm. We describe this algorithm and give experimental results conducted on a 128-processor Cray T3E. We show that our parallel algorithm is able to efficiently compute partitionings of similar edge-cuts as serial multi-constraint algorithms, and can scale to very large graphs. Our parallel multi-constraint graph partitioner is able to compute a three-constraint 128-way partitioning of a 7.5 million node graph in about 7 seconds on 128 processors of a Cray T3E.