Here, we develop a model to optimize the location of public fast charging stations for electric vehicles (EVs). A difficulty in planning the placement of charging stations is uncertainty in where EV charging demands appear. For this reason, we use a stochastic flow-capturing location model (SFCLM). A sample-average approximation method and an averaged two-replication procedure are used to solve the problem and estimate the solution quality. We demonstrate the use of the SFCLM using a Central-Ohio based case study. We find that most of the stations built are concentrated around the urban core of the region. As the number of stations built increases, some appear on the outskirts of the region to provide an extended charging network. We find that the sets of optimal charging station locations as a function of the number of stations built are approximately nested. We demonstrate the benefits of the charging-station network in terms of how many EVs are able to complete their daily trips by charging midday?six public charging stations allow at least 60% of EVs that would otherwise not be able to complete their daily tours without the stations to do so. We finally compare the SFCLM to a deterministic model, in which EV flows are set equal to their expected values. We show that if a limited number of charging stations are to be built, the SFCLM outperforms the deterministic model. As the number of stations to be built increases, the SFCLM and deterministic model select very similar station locations.