Creativity is a major source of innovation, growth, adaptability, and psychological resilience, making it a top priority of governments, global corporations, educational institutions, and other organizations that collectively invest hundreds of millions of dollars annually into training. The current foundation of creativity training is the technique known as divergent thinking; yet for decades, concerns have been raised about the adequacy of divergent thinking: it is incongruent with the creative processes of children and most adult creatives, and it has failed to yield expected downstream results in creative production. In this article, we present an alternative approach to creativity training, based in neural processes different from those involved in divergent thinking and drawing upon a previously unused resource for creativity research: narrative theory. We outline a narrative theory of creativity training; illustrate with examples of training and assessment from our ongoing work with the U.S. Department of Defense, Fortune 50 companies, and graduate and professional schools; and explain how the theory can help fill prominent lacunae and gaps in existing creativity research, including the creativity of children, the psychological mechanisms of scientific and technological innovation, and the failure of computer artificial intelligence to replicate human creativity.