We describe our experience in obtaining significant computational improvements in the solution of large stochastic unit commitment problems. The model we use is a stochastic version of a planning model used by the California Independent System Operator, covering the entire WECC western regional grid. We solve daily hour-timestep stochastic unit commitment problems using a new progressive hedging approach that features linear subproblems and guided solves for finding feasible solutions. For stochastic problems with 5 scenarios, the algorithm produces near-optimal solutions with a 6 times improvement in serial solution time, and over 20 times improvement when run in parallel; for previously unsolvable stochastic problems, we obtain near-optimal solutions within a couple of hours. We note that although this algorithm is demonstrated for stochastic unit commitment problems, the algorithm itself is suitable for application to generic stochastic optimization problems.