Complexity theory is a field of physics that studies the nature and behavior of complex systems, systems whose elements interact in complex and unpredictable ways. Recent years have seen a number of attempts to extend its scope to the biological and social sciences, and now Larsen-Freeman and Cameron offer a view of applied linguistics from a complexity perspective, claiming to show the relevance of the theory to various aspects of the language sciences. In this review of their book I look at their claims, and point out some of the reasons why these claims do not hold. (Contains 5 notes.)