Despite revolutionary claims about the changing shape of organizations and strategy, the predispositions of executives are often framed and limited by the structures assumed by strategy's foundational works of the 1960s. These works emphasize top-down planning, generic linear processes, simple either/or choices, and singular outcomes. We argue that there is a need to evolve these mental frames to better enable executives to appreciate how today's firms can compete more effectively through individualized approaches that seek both economies of scale and unique identities in the marketplace. This evolution necessitates a new framework that can handle complex, multi-dimensional processes. Such a generic framework would conceptualize the need to simultaneously customize products and services for individual consumers while trying to reduce costs through efficient production and service provision. In working with executives in Europe and Australia, we have drawn upon the chimera, a creature with a single body and different formidable heads operating on many fronts, as an analogy for the firm confronting numerous, quite different, and often paradoxical challenges. The chimera has inspired us to create a new framework: the Value Chimera--a multi-faceted, multi-dimensional means of assessing how firms can manage their value-adding processes to target multiple customer groups in complex business environments.