This paper describes and offers a corrective for problematic implications of classic paradigms of serendipitous discovery in science, such as the narrative that Fleming discovered penicillin. As usually told, an individual (Fleming) makes an isolated observation by chance (of mould in his petri dish) which leads inevitably to a major discovery. Such stories leave out important interactions—emerging networks—that were equally important. Further, they perpetuate the mistaken belief that the epistemology of discovery is mysterious. By reforming the paradigm, I provide a social-epistemological grounding for the role of chance in science, and for the development of a skill-based epistemology of discovery.