Electric vehicles are gaining importance and help to reduce dependency on oil, increase energy efficiency of transportation, reduce carbon emissions and noise, and avoid tail pipe emissions. Because of short driving distances, high mileages, and intermediate waiting times, fossil-fuelled taxi vehicles are ideal candidates for being replaced by battery electric vehicles (BEVs). Moreover, taxis as BEVs would increase visibility of electric mobility and therefore encourage others to purchase an electric vehicle. Prior to replacing conventional taxis with BEVs, a suitable charging infrastructure has to be established. This infrastructure, which is a prerequisite for the use of BEVs in practice, consists of a sufficiently dense network of charging stations taking into account the lower driving ranges of BEVs. In this case study we propose a decision support system for placing charging stations to satisfy the charging demand of electric taxi vehicles. Operational taxi data from about 800 vehicles is used to identify and estimate the charging demand for electric taxis based on frequent origins and destinations of trips. Next, a variant of a set covering problem is formulated and solved, aiming at satisfying as much charging demand as possible with a limited number of charging stations. Already existing charging locations are considered in the optimization problem. In this work, we focus on finding regions in which charging stations should be placed, rather than exact locations. The exact location within an area is identified in a post-optimization phase (e.g., by authorities), where environmental conditions are considered, e.g., the capacity of the power network, availability of space, and legal issues. Our approach is implemented in the city of Vienna, Austria, in the course of an applied research project conducted in 2014. Local authorities, power network operators, representatives of taxi driver guilds as well as a radio taxi provider participated in the project and identified exact locations for charging stations based on our decision support system.