When laser radiation is skilfully applied, atoms and molecules can be cooled1–3, allowing the precise measurements and control of quantum systems. This is essential for the fundamental studies of physics as well as practical applications such as precision spectroscopy4–7, ultracold gases with quantum statistical properties8–10 and quantum computing. In laser cooling, atoms are slowed to otherwise unattainable velocities through repeated cycles of laser photon absorption and spontaneous emission in random directions. Simple systems can serve as rigorous testing grounds for fundamental physics—one such case is the purely leptonic positronium11,12, an exotic atom comprising an electron and its antiparticle, the positron. Laser cooling of positronium, however, has hitherto remained unrealized. Here we demonstrate the one-dimensional laser cooling of positronium. An innovative laser system emitting a train of broadband pulses with successively increasing central frequencies was used to overcome major challenges posed by the short positronium lifetime and the effects of Doppler broadening and recoil. One-dimensional chirp cooling was used to cool a portion of the dilute positronium gas to a velocity distribution of approximately 1 K in 100 ns. A major advancement in the field of low-temperature fundamental physics of antimatter, this study on a purely leptonic system complements work on antihydrogen13, a hadron-containing exotic atom. The successful application of laser cooling to positronium affords unique opportunities to rigorously test bound-state quantum electrodynamics and to potentially realize Bose–Einstein condensation14–18 in this matter–antimatter system.