How the world's 6,000+ natural languages have arisen is mostly unknown. Yet, new sign languages have emerged recently among deaf people brought together in a community, offering insights into the dynamics of language evolution. However, documenting the emergence of these languages has mostly consisted of studying the end product; the process by which ad hoc signs are transformed into a structured communication system has not been directly observed. Here we show how young children create new communication systems that exhibit core features of natural languages in less than 30 min. In a controlled setting, we blocked the possibility of using spoken language. In order to communicate novel messages, including abstract concepts, dyads of children spontaneously created novel gestural signs. Over usage, these signs became increasingly arbitrary and conventionalized. When confronted with the need to communicate more complex meanings, children began to grammatically structure their gestures. Together with previous work, these results suggest that children have the basic skills necessary, not only to acquire a natural language, but also to spontaneously create a new one. The speed with which children create these structured systems has profound implications for theorizing about language evolution, a process which is generally thought to span across many generations, if not millennia.