In this paper, a computationally efficient chance-constrained rollover-free motion planning method is presented. Specifically, the method is developed to plan motions for reconfigurable vehicles with the knowledge of a 3-D terrain model that has limited accuracy. The overall motion planning problem is formulated as a nonlinear optimal control problem (NOCP) that employs a constraint in the form of a bound on the probability of rollover under terrain-induced vehicle orientation uncertainty. To increase the computational efficiency of the NOCP, a geometric interpretation of the chance constraint is derived based on the characteristics of SO(3), the 3-D rotation group. Monte Carlo simulations are provided to demonstrate the usefulness of the geometric interpretation through comparisons with other methods. Experimental data gathered from driving a mobile robot through real forests are also used to validate the proposed model. Finally, path and trajectory generation results obtained with the proposed planning method for a feller-buncher machine traversing through uncertain 3-D terrain are presented to showcase the method’s overall performance and efficiency.