We describe an implementation of a compact parallel algorithm for 3D Delaunay tetrahedralization on a 64-processor shared-memory machine. Our algorithm uses a concurrent version of the Bowyer-Watson incremental insertion, and a thread-safe space-efficient structure for representing the mesh. Using the implementation we are able to generate significantly larger Delaunay meshes than have previously been generated—10 billion tetrahedra on a 64 processor SMP using 200GB of RAM.The implementation makes use of a locality based relabeling of the vertices that serves three purposes—it is used as part of the space efficient representation, it improves the memory locality, and it reduces the overhead necessary for locks. The implementation also makes use of a caching technique to avoid excessive decoding of vertex information, a technique for backing out of insertions that collide, and a shared work queue for maintaining points that have yet to be inserted.