In recent years parallel computing on a fast network of high performance and low cost workstations has become a viable and an economic option, compared to that on an expensive high performance parallel supercomputer for solving large Grand Challenge scientific problems. This paper focuses on how to efficiently exploit the computing resources of a set of heterogeneous Unix workstations. We have further developed the CHARM parallel programming environment to allow programs written in the CHARM language execute adjacently on such a cluster. We have also developed a new scheme to schedule tasks statically and balance the load dynamically to achieve high effective utilization. Performance results for several applications programs including ray-tracing, all-pairs shortest path, and matrix multiply on a heterogeneous cluster of Sun Sparcs, IBM RS/6000s and HP-PA 7100s show a significant improvement in execution time over sequential execution.>