Lightning is a dangerous yet poorly understood natural phenomenon. Lightning forms a network of plasma channels propagating away from the initiation point with both positively and negatively charged ends—called positive and negative leaders1. Negative leaders propagate in discrete steps, emitting copious radio pulses in the 30-300-megahertz frequency band2-8 that can be remotely sensed and imaged with high spatial and temporal resolution9-11. Positive leaders propagate more continuously and thus emit very little high-frequency radiation12. Radio emission from positive leaders has nevertheless been mapped13-15, and exhibits a pattern that is different from that of negative leaders11-13,16,17. Furthermore, it has been inferred that positive leaders can become transiently disconnected from negative leaders9,12,16,18-20, which may lead to current pulses that both reconnect positive leaders to negative leaders11,16,17,20-22 and cause multiple cloud-to-ground lightning events1. The disconnection process is thought to be due to negative differential resistance18, but this does not explain why the disconnections form primarily on positive leaders22, or why the current in cloud-to-ground lightning never goes to zero23. Indeed, it is still not understood how positive leaders emit radio-frequency radiation or why they behave differently from negative leaders. Here we report three-dimensional radio interferometric observations of lightning over the Netherlands with unprecedented spatiotemporal resolution. We find small plasma structures—which we call `needles'—that are the dominant source of radio emission from the positive leaders. These structures appear to drain charge from the leader, and are probably the reason why positive leaders disconnect from negative ones, and why cloud-to-ground lightning connects to the ground multiple times.