A common vision from science fiction is that robots will one day inhabit our physical spaces, sense the world as we do, assist our physical labours, and communicate with us through natural language. Here we study how to design artificial agents that can interact naturally with humans using the simplification of a virtual environment. We show that imitation learning of human-human interactions in a simulated world, in conjunction with self-supervised learning, is sufficient to produce a multimodal interactive agent, which we call MIA, that successfully interacts with non-adversarial humans 75% of the time. We further identify architectural and algorithmic techniques that improve performance, such as hierarchical action selection. Altogether, our results demonstrate that imitation of multi-modal, real-time human behaviour may provide a straightforward and surprisingly effective means of imbuing agents with a rich behavioural prior from which agents might then be fine-tuned for specific purposes, thus laying a foundation for training capable agents for interactive robots or digital assistants. A video of MIA’s behaviour may be found here.