Quantum computers exploit the quantum nature of physical systems to perform computations. While we have yet to build a large-scale quantum computer, we can prove that such devices would have an advantage over standard computers for some problems. However, there are still many tasks for which we don't have a good understanding of the performance of quantum computers. For example, how well can a quantum computer play chess? In this talk, I will describe a quantum algorithm for playing simple, two-player games.