Emerging science and technology fields are increasingly expected to provide solutions to societal grand challenges. The promise of such solutions frequently underwrites claims for the public funding of research. In parallel, universities, public research organizations and, in particular, private enterprises draw on such research to actively secure property rights over potential applications through patenting. Patents represent a claim to garner financial returns from the novel outcomes of science and technology. This is justified by the potential social value promised by patents as they encourage information sharing, further R&D investment, and the useful application of new knowledge. Indeed, the value of patents has generated longstanding academic interest in innovation studies with many scholars investigating its determinants based on econometric models. Yet, this research has largely focused on evaluating factors that influence the market value of patents and the gains from exclusivity rights granted to inventions, which reflect the private value of a patent. However, the patent system is a socially shaped enterprise where private and public concerns intersect. Despite the notion of the social utility of inventions as a patenting condition, and evidence of disconnection between societal needs and the goals of private actors, less attention has been paid to other interpretations of patent value. This paper investigates the various articulations of value delineated by patents in an emerging science and technology domain. As a pilot study, we analyse patents in synthetic biology, contributing a new analytical framework and classification of private and public values at the intersections of science, economy, and society. After considering the legal, business, social and political dimensions of patenting, we undertake a qualitative and systematic examination of patent content in synthetic biology. Our analysis probes the private and public value propositions that are framed in these patents in terms of the potential private and public benefits of research and innovation. Based on this framework, we shed light on questions of what values are being nurtured in inventions in synthetic biology and discuss how attention to public as well as private values opens up promising avenues of research in science, technology and innovation policy.