Global Positioning System (GPS) measurements at subduction plate boundaries often record fault movements similar to earthquakes but much slower, occurring over timescales of ∼1 week to ∼1 year. These 'slow slip events' have been observed in Japan1,2, Cascadia3-7, Mexico8,9, Alaska10and New Zealand11. The phenomenon is poorly understood, but several observations hint at the processes underlying slow slip. Although slip itself is silent, seismic instruments often record coincident low-amplitude tremor in a narrow (1-5 cycles per second) frequency range12. Also, modelling of GPS data3,7,9and estimates of tremor location13indicate that slip focuses near the transition from unstable ('stick-slip') to stable friction at the deep limit of the earthquake-producing seismogenic zone. Perhaps most intriguingly, slow slip is periodic at several locations, with recurrence varying from 6 to 18 months depending on which subduction zone (or even segment) is examined4-6,9. Here I show that such periodic slow fault slip may be a resonant response to climate-driven stress perturbations. Fault slip resonance helps to explain why slip events are periodic, why periods differ from place to place, and why slip focuses near the base of the seismogenic zone. Resonant slip should initiate within the rupture zone of future great earthquakes, suggesting that slow slip may illuminate fault properties that control earthquake slip.