As chip multiprocessors proliferate, programming support for these devices is likely to receive a lot of attention in the near future. Parallelism and data locality are two critical issues in a chip multiprocessor environment. Unfortunately, most of the published work in the literature focuses only on one of these problems, and this can prevent one from achieving the best possible performance. The main goal of this paper is to propose and evaluate a compiler-directed code parallelization scheme, which considers both parallelism and data locality at the same time. Our compiler captures the inherent parallelism and data reuse in the application code being analyzed using a novel representation called the locality-parallelism graph (LPG). Our partitioning/scheduling algorithm assigns the nodes of this graph to the processors in the architecture and schedules them for execution. We implemented this algorithm and evaluated its effectiveness using a set of benchmark codes. The results collected so far indicate that our approach improves overall execution latency significantly. In this paper, we also introduce an ILP (Integer Linear Programming) based formulation of the problem, and implement the schedule obtained by the ILP solver. The results indicate that our approach gets within 4% of the ILP solution.