Both science itself, and the human culture of which it is a part, would benefit from a story of science that encourages wider engagement with and participation in the processes of scientific exploration. Such a story, based on a close analysis of scientific method, is presented here. It is the story of science as story telling and story revising. The story of science as story suggests that science can and should serve three distinctive functions for humanity: providing stories that may increase (but never guarantee) human well-being, serving as a supportive nexus for human exploration and story telling in general, and exemplifying a commitment to skepticism and a resulting open-ended and continuing exploration of what might yet be. Some practical considerations that would further the development and acceptance of such a story of science as a widely shared nexus of human activity are described.