For many years, creativity research had been yielding contradictory results. More recently, these results have come to be regarded as creativity paradoxes. This research reviews a growing body of evidence that highly creative people tend to operate, either simultaneously or dynamically, at extremes along continuums, where the extremes are considered at odds with one another. More highly creative people, it seems, tend to find a middle way, not by operating at a mid-point along a continuum, but by operating at and blending two more-extreme positions. An argument is presented that this is consistent with complexity theory, particularly the "order-chaos dynamic" characteristic of Complex Adaptive Systems (CASs), and that the number of paradoxes discovered in creativity research provides evidence for creativity being a characteristic of CASs. Understanding creativity as a characteristic of CASs leads to a new view of creativity and innovation, which could result in better creativity enhancement and innovation management approaches while also leading to improved tools to identify highly creative individuals.