The central aim of this paper is to undertake a critical review of arguments which propose that chess should be taught in schools and other educational settings. In particular, I offer an answer to the question: "Should chess be taught in early childhood?" Many claims have been made about the educational benefits of chess instruction. In evaluating these, I argue that critics of such claims have neglected an important possibility for evaluating the teaching of chess: undertaking research studies that employ an action research (AR) methodology. This paper focuses on the following themes: (1) chess: the gymnasium of the mind; (2) teaching and learning chess: the current context; (3) teaching young children to play chess: some common claims; (4) research studies and "the ideal experiment"; (5) teaching chess: the role of AR and (6) conclusion: should chess be taught in early childhood?