Let be an affine Weyl group, and let be a left, right, or two-sided Kazhdan-Lusztig cell in . Let be the set of all reduced expressions of elements of , regarded as a formal language in the sense of the theory of computation. We show that is a regular language. Hence, the reduced expressions of the elements in any Kazhdan-Lusztig cell can be enumerated by a finite state automaton.