Epithelial organoids, such as those derived from stem cells of the intestine, have great potential for modelling tissue and disease biology1-4. However, the approaches that are used at present to derive these organoids in three-dimensional matrices5,6 result in stochastically developing tissues with a closed, cystic architecture that restricts lifespan and size, limits experimental manipulation and prohibits homeostasis. Here, by using tissue engineering and the intrinsic self-organization properties of cells, we induce intestinal stem cells to form tube-shaped epithelia with an accessible lumen and a similar spatial arrangement of crypt- and villus-like domains to that in vivo. When connected to an external pumping system, the mini-gut tubes are perfusable; this allows the continuous removal of dead cells to prolong tissue lifespan by several weeks, and also enables the tubes to be colonized with microorganisms for modelling host-microorganism interactions. The mini-intestines include rare, specialized cell types that are seldom found in conventional organoids. They retain key physiological hallmarks of the intestine and have a notable capacity to regenerate. Our concept for extrinsically guiding the self-organization of stem cells into functional organoids-on-a-chip is broadly applicable and will enable the attainment of more physiologically relevant organoid shapes, sizes and functions.