The paper develops a solution method for scheduling units of a power-generating system to produce electricity by taking into consideration the stochasticity of the hourly load and its correlation structure. The unit commitment problem is initially formulated as a chance-constrained optimization problem in which we require that the load be met with a specified high probability over the entire time horizon. The solution procedure consists of solving a sequence of deterministic versions of the unit commitment problem that converge to the solution of the chance constrained program. For the deterministic unit commitment problems, Lagrangian relaxation is used to separate the dual problem into its subproblems. Each subproblem is solved by a dynamic program. The initial results indicate that accounting for the correlation structure of the hourly loads reduces the value of the objective function when the optimization problem is formulated as a chance constrained program. Monte Carlo simulation is used to verify the accuracy of the solution provided by the algorithm. The relationship that the unit commitment solution found using the chance constrained optimization approach has with that found using conventional optimization spinning reserves is discussed.