  We describe a version of an algorithm for evolving self-gravitating
collections of particles that should be nearly ideal for parallel
architectures. Our method is derived from the ``self-consistent field'' (SCF)
approach suggested previously by Clutton-Brock and others. Owing to the use of
a global description of the gravitational field, the particles in an SCF
simulation do not interact with one another directly, minimizing communications
overhead between nodes in a parallel implementation. Ideal load-balancing is
achieved since precisely the same number of operations are needed to compute
the acceleration for each particle. Consequently, the SCF technique is
perfectly scalable and the size of feasible applications will grow in simple
proportion to advances in computational hardware. We describe an SCF code
developed for and tested on a Connection Machine 5. Empirical tests demonstrate
the efficient and scalable nature of the algorithm. Depending on the
application, simulations with particle numbers in the range $N\sim 10^7 -
10^{8.5}$ are now possible. Larger platforms should make simulations with
billions of particles feasible in the near future. Specific astrophysical
applications are discussed in the context of collisionless dynamics.
