Previous studies have reported an association between preterm birth and elevated blood pressure in adolescence and young adulthood. These studies were based on single-day blood pressure measurements and had limited ability to estimate risk of hypertension measured over a longer period and across the full range of gestational ages. The authors conducted a national cohort study of all infants born in Sweden from 1973 through 1979 (n = 636,552), including 28,220 born preterm (<37 weeks), followed to ages 25.5-37.0 years to determine whether individuals born preterm were more likely to be prescribed antihypertensive medications in 2005-2009 than those born full term. Antihypertensive medication data were obtained from all outpatient and inpatient pharmacies throughout Sweden. Young adults who were born preterm had an increased relative rate of antihypertensive medication prescription that increased monotonically by earlier gestational age and that was independent of fetal growth. The adjusted odds ratio for ≥1 antihypertensive medications/year ranged from 1.25 (95% confidence interval: 1.12, 1.39) for those born near term (35-36 weeks) to 2.51 (95% confidence interval: 1.11, 5.68) for those born extremely preterm (23-27 weeks) relative to those born full term. These findings suggest that preterm birth is strongly associated with hypertension in young adulthood, including an increased risk among those born near term.