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Multi-core CPUs with multiple levels of parallelism and deep memory hierarchies have become the mainstream computing platform. In this paper we developed a generally applicable high performance computing framework for Monte Carlo simulation (MCS) type applications in distribution systems, taking advantage of performance-enhancing features of multi-core CPUs. The application in this paper is to solve the probabilistic load flow (PLF) in real time, in order to cope with the uncertainties caused by the integration of renewable energy resources. By applying various performance optimizations and multi-level parallelization, the optimized MCS solver is able to achieve more than 50% of a CPU's theoretical peak performance and the performance is scalable with the hardware parallelism. We tested the MCS solver on the IEEE 37-bus test feeder using a new Intel Sandy Bridge multi-core CPU. The optimized MCS solver is able to solve millions of load flow cases within a second, enabling the real-time Monte Carlo solution of the PLF.