As autonomous systems tackle more real-world situations, mission success oftentimes cannot be guaranteed and the planner must reason about the probability of failure. Unfortunately, computing a trajectory that satisfies mission goals while constraining the probability of failure is difficult because of the need to reason about complex, multidimensional probability distributions. Recent methods have seen success using chance-constrained, model-based planning. We argue there are two main drawbacks to these approaches. First, current methods suffer from an inability to deal with expressive environment models such as 3D non-convex obstacles. Second, most planners rely on considerable simplifications when computing trajectory risk including approximating the agent's dynamics, geometry, and uncertainty. We apply hybrid search to the risk-bound, goal-directed planning problem. The hybrid search consists of a region planner and a trajectory planner. The region planner makes discrete choices by reasoning about geometric regions that the agent should visit in order to accomplish its mission. In formulating the region planner, we propose landmark regions that help produce obstacle-free paths. The region planner passes paths through the environment to a trajectory planner; the task of the trajectory planner is to optimize trajectories that respect the agent's dynamics and the user's desired risk of mission failure. We discuss three approaches to modeling trajectory risk: a CDF-based approach, a sampling-based collocation method, and an algorithm named Shooting Method Monte Carlo. A variety of 2D and 3D test cases are presented in the full paper including a linear case, a Dubins car model, and an underwater autonomous vehicle. The method is shown to outperform other methods in terms of speed and utility of the solution. Additionally, the models of trajectory risk are shown to better approximate risk in simulation.