Loneliness is a complex biological trait that has been associated with numerous negative health outcomes. The measurement and environmental determinants of loneliness are well understood, but its genetic basis is not. Previous studies have estimated the heritability of loneliness between 37 and 55% using twins and family-based approaches, and have explored the role of specific candidate genes. We used genotypic and phenotypic data from 10 760 individuals aged ⩾50 years that were collected by the Health and Retirement Study (HRS) to perform the first genome-wide association study of loneliness. No associations reached genome-wide significance (p>5 × 10-8). Furthermore, none of the previously published associations between variants within candidate genes (BDNF, OXTR, RORA, GRM8, CHRNA4, IL-1A, CRHR1, MTHFR, DRD2, APOE) and loneliness were replicated (p>0.05), despite our much larger sample size. We estimated the chip heritability of loneliness and examined coheritability between loneliness and several personality and psychiatric traits. Our estimates of chip heritability (14-27%) support a role for common genetic variation. We identified strong genetic correlations between loneliness, neuroticism, and a scale of 'depressive symptoms.' We also identified weaker evidence for coheritability with extraversion, schizophrenia, bipolar disorder, and major depressive disorder. We conclude that loneliness, as defined in this study, is a modestly heritable trait that has a highly polygenic genetic architecture. The coheritability between loneliness and neuroticism may reflect the role of negative affectivity that is common to both traits. Our results also reflect the value of studies that probe the common genetic basis of salutary social bonds and clinically defined psychiatric disorders.