Four small moons—Styx, Nix, Kerberos and Hydra—follow near-circular, near-equatorial orbits around the central ‘binary planet’ comprising Pluto and its large moon, Charon. New observational details of the system have emerged following the discoveries of Kerberos and Styx. Here we report that Styx, Nix and Hydra are tied together by a three-body resonance, which is reminiscent of the Laplace resonance linking Jupiter’s moons Io, Europa and Ganymede. Perturbations by the other bodies, however, inject chaos into this otherwise stable configuration.