The genome has become a crucial component in precision medicine aimed at tailoring medical treatment to the individual. To the extent that social science studies of genomics have explored questions related to the individual, these studies have focused on how the governance regarding genomes facilitates individuals’ rights, choices, and responsibilities. By contrast, we approach genomic governance by investigating how enactments of the person in precision medicine actualize practices of reciprocity and belonging in a national collective. Based on document analysis and ethnographic fieldwork in Denmark, we show that genomes are treated simultaneously as digital representations of individuals, social resources for a welfare state population, and emblems of public trust. By drawing on classical and contemporary anthropological theories of personhood, we unfold how Danish precision medicine prescribes a moral continuity between person, state, and territory. We argue that Danish precision medicine revitalizes a national politics of belonging and generates socio-spatial orientations through which the “me” of the person shares origin and place with the “we” of the welfare state.