We propose an extraction schedule for the Chuquicamata underground copper mine in Chile. The schedule maximizes profits while adhering to all operational and geomechanical requirements involved in proper removal of the material. We include extraction capacity uncertainties due to failure in equipment, specifically to the overland conveyor, which we find to be the most critical component in the extraction process. First we present the extraction plan based on a deterministic model, which does not assume uncertainty in the extraction capacity and represents the solution that the mine can implement without using the results of this study. Then we extend this model to a stochastic setting by generating different scenarios for capacity values in subsequent periods. We construct a multistage model that handles economic downside risk arising from this uncertainty by penalizing plans that deviate from an ex ante profit target in one or more scenarios. Simulation results show that a stochastic-based solution can achieve the same expected profits as the deterministic-based solution. However, the earnings of the stochastic-based solution average 5% more for scenarios in which earnings are below the 10th percentile. If we choose a target 2% below the expected profit obtained by the deterministic-based solution, this average increases from 5% to 9%.