We study the problem of adversarial language games, in which multiple agents with conflicting goals compete with each other via natural language interactions. While adversarial language games are ubiquitous in human activities, little attention has been devoted to this field in natural language processing. In this work, we propose a challenging adversarial language game called Adversarial Taboo as an example, in which an attacker and a defender compete around a target word. The attacker is tasked with inducing the defender to utter the target word invisible to the defender, while the defender is tasked with detecting the target word before being induced by the attacker. In Adversarial Taboo, a successful attacker and defender need to hide or infer the intention, and induce or defend during conversations. This requires several advanced language abilities, such as adversarial pragmatic reasoning and goal-oriented language interactions in open domain, which will facilitate many downstream NLP tasks. To instantiate the game, we create a game environment and a competition platform. Comprehensive experiments on several baseline attack and defense strategies show promising and interesting results, based on which we discuss some directions for future research.