The United States’ ambitious Precision Medicine Initiative proposes to accelerate exponentially the adoption of precision medicine, an approach to health care that tailors disease diagnosis, treatment, and prevention to individual variability in genes, environment, and lifestyle. It aims to achieve this by creating a cohort of volunteers for precision medicine research, accelerating biomedical research innovation, and adopting policies geared toward patients’ empowerment. As strategies to implement the PMI are formulated, critical consideration of the initiative's ethical and sociopolitical dimensions is needed. Drawing on scholarship of nationalism and democracy, we discuss the PMI's construction of what we term “genomic citizenship”; the possible normative obligations arising therefrom; and the ethical, legal, and social challenges that will ensue. Although the PMI is a work in progress, discussion of the existing and emerging issues can facilitate the development of policies, structures, and procedures that can maximize the initiative's ability to produce equitable and socially sensitive outcomes. Our analysis can also be applied to other population‐based, precision medicine research programs.