Spintronics relies on the transport of spins, the intrinsic angular momentum of electrons, as an alternative to the transport of electron charge as in conventional electronics. The long-term goal of spintronics research is to develop spin-based, low-dissipation computing-technology devices. Recently, long-distance transport of a spin current was demonstrated across ferromagnetic insulators1. However, antiferromagnetically ordered materials, the most common class of magnetic materials, have several crucial advantages over ferromagnetic systems for spintronics applications2: antiferromagnets have no net magnetic moment, making them stable and impervious to external fields, and can be operated at terahertz-scale frequencies3. Although the properties of antiferromagnets are desirable for spin transport4-7, indirect observations of such transport indicate that spin transmission through antiferromagnets is limited to only a few nanometres8-10. Here we demonstrate long-distance propagation of spin currents through a single crystal of the antiferromagnetic insulator haematite (α-Fe2O3)11, the most common antiferromagnetic iron oxide, by exploiting the spin Hall effect for spin injection. We control the flow of spin current across a haematite-platinum interface-at which spins accumulate, generating the spin current-by tuning the antiferromagnetic resonance frequency using an external magnetic field12. We find that this simple antiferromagnetic insulator conveys spin information parallel to the antiferromagnetic Néel order over distances of more than tens of micrometres. This mechanism transports spins as efficiently as the most promising complex ferromagnets1. Our results pave the way to electrically tunable, ultrafast, low-power, antiferromagnetic-insulator-based spin-logic devices6,13 that operate without magnetic fields at room temperature.