This article uses a contemporary and revelatory case study to explore the relationship between three conversations in the innovation literature: Design Thinking, creativity in strategy, and the emerging area of Art Thinking. Businesses are increasingly operating in a VUCA environment where they need to design better experiences for their customers and better outcomes for their firm and the Arts are no exception. Innovation, or more correctly, growth through innovation, is a top priority for business and although there is no single, unifying blueprint for success at innovation, Design Thinking is the process that is receiving most attention and getting most traction. We review the literature on Design Thinking, showing how it teaches businesses to think with the creativity and intuition of a designer to show a deep understanding of, and have empathy with, the user. However, Design Thinking has limitations. By placing the consumer at the very heart of the innovation process, Design Thinking can often lead to more incremental, rather than radical, ideas. Now there is a new perspective emerging, Art Thinking, in which the objective is not to design a journey from the current scenario, A, to an improved position, A+. Art Thinking requires the creation of an optimal position B, and spends more time in the open-ended problem space, staking out possibilities and looking for uncontested space. This paper offers a single case study of a national arts organisation in Dublin facing an existential crisis, which used an Art Thinking approach successfully to give a much-needed shot in the arm to its commercial innovation activities.