The devil's staircase -- a continuous function on the unit interval [0,1] which is not constant, yet is locally constant on an open dense set -- is the sort of exotic creature a combinatorialist might never expect to encounter in ``real life.'' We show how a devil's staircase arises from the combinatorial problem of parallel chip-firing on the complete graph. This staircase helps explain a previously observed ``mode locking'' phenomenon, as well as the surprising tendency of parallel chip-firing to find periodic states of small period.