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This paper describes a new extension to the rapidly-exploring random tree (RRT) path planning algorithm. The particle RRT algorithm explicitly considers uncertainty in its domain, similar to the operation of a particle filter. Each extension to the search tree is treated as a stochastic process and is simulated multiple times. The behavior of the robot can be characterized based on the specified uncertainty in the environment, and guarantees can be made as to the performance under this uncertainty. Extensions to the search tree, and therefore entire paths, may be chosen based on the expected probability of successful execution. The benefit of this algorithm is demonstrated in the simulation of a rover operating in rough terrain with unknown coefficients of friction