We describe a novel, university-level, introductory biology course that uses evolution as a narrative framework. Our course conveys the content in an introductory biology course by telling the story of the evolution of life on Earth. We begin with early Earth environments in which biological molecules and processes evolved and led to the first RNA-based living entities, then to DNA-based cells, and then to all of the life around us. We use this framework to describe the evolution of the physiological processes important for beginning biology students. This structure contrasts with the widespread "levels of organization" approach in which the order of topics treats the molecular level first, then cells and organisms, and finally evolutionary and ecological processes. This traditional approach is limited in at least two ways: (1) The material taught at each level is not explicitly connected to that at other levels, making the concepts more difficult to assimilate and retain; and (2) Evolution is taught as a discrete section of the course, rather than as the integrating principle of life itself. We find that our narrative evolutionary approach enables students to more effectively assimilate, retain, and connect the vast amount of information presented in an introductory biology course.