Chimera states occur when a network of identical oscillators splits into two groups, one consisting of synchronous oscillators, the other of partially-synchronous oscillators. We show how to analyze such states when the oscillators are not identical, using the recent ansatz of Ott and Antonsen to derive non-local differential equations governing the network dynamics in the continuum limit. The same techniques can be used to study transient fronts which connect regions of high synchrony with regions of asynchrony.