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 -- might appear at first glance as an idle curiosity or an obscure counterexample in analysis. Certainly a combinatorialist would never expect to encounter such an exotic creature in "real life." We show how a devil's staircase arises from the combinatorial problem of parallel chip-firing on the complete graph. Moreover, this staircase helps explain the surprising tendency of parallel chip-firing to find periodic states of small period.