We apply a stochastic method introduced by Dellago et al. [J. Chem. Phys. 108, 1964 (1998)] to sample transition paths in high-dimensional systems. The method connects two endpoint regions (for example a reactant and a product region) by a set of space-time paths. This approach is an importance sampling for rare events that does not require prior knowledge of the location of dynamical bottlenecks. Transition paths are generated with a weight corresponding to a chain of Metropolis Monte Carlo steps. We derive Monte Carlo algorithms and apply the technique to the dynamics of hydrogen-bond breaking in liquid water. We obtain averages in a transition path ensemble for the;structure: and energy along,the trajectory. While characterized by a rate constant, hydrogen-bond breaking in water occurs frequently enough to be studied by standard methods. The process therefore provides a useful test of path sampling methods. The comparison between path sampling and standard Monte Carlo demonstrate the feasibility of transition pad; sampling for a many-body system with a rough potential energy surface.