This article presents work in progress towards a better understanding of the origins of narrative. Assuming an evolutionary and developmental continuity of mental experiences, we propose a grounding of human narrative capacities in non-verbal narrative transactions in non-human animals, and in pre-verbal narrative transactions of human children. We discuss narrative intelligence in the context of the evolution of primate (social) intelligence, and with respect to the particular cognitive limits that constrain the development of human social networks and societies. We explain the Narrative Intelligence Hypothesis which suggests that the evolutionary origin of communicating in a narrative format co-evolved with increasingly complex social dynamics among our human ancestors. This article gives examples of social interactions in non-human primates and how these can be interpreted in terms of narrative formats. Due to the central role of narrative in human communication and social interaction, we discuss how research into the origins of narrative can impact the development of humane technology which is designed to meet the biological, cognitive and social needs of human story-tellers.