In this paper, I assume that the study of the origin of language is strictly connected to the analysis of the traits that distinguish human language from animal communication. Usually, human language is said to be unique in the animal kingdom because it enables and/or requires intentionality or mindreading. By emphasizing the importance of mindreading, the social brain hypothesis has provided major insights within the origin of language debate. However, as studies on non-human primates have demonstrated that intentional forms of communication are already present in these species to a greater or lesser extent, I maintain that the social brain is a necessary but not a sufficient condition to explain the uniqueness of language. In this paper, I suggest that the distinctive feature of human communication resides in the ability to tell stories, and that the origin of language should be traced with respect to the capacity to produce discourses, rather than phrases or words. As narrative requires the ability to link events distant from one another in space and time, my proposal is that in order to explain the origin of language, we need to appeal to both the social brain and the ecological brain – that is, the cognitive devices which allow us to mentally travel in space and time.