Background While recent cross‐sectional research has documented a relationship between sleep problems and antisocial behavior, the longitudinal nature of this relationship is unknown. This study tests both the hypothesis that adolescent daytime sleepiness is associated with later adult criminal offending, and also tests a biopsychosocial mediation model in which social adversity predisposes to sleepiness, which in turn predisposes to attentional impairment, and to adult crime. Methods Schoolboys aged 15 years rated themselves on self‐report sleepiness. Age 15 antisocial behavior was assessed by teacher ratings and self‐reports, while convictions for crime were assessed at age 29. Attentional capacity at age 15 was assessed by autonomic orienting, with arousal assessed by the electroencephalogram (EEG). Results Sleepy adolescents were more likely to be antisocial during adolescence, and were 4.5 times more likely to commit crime by age 29. The sleepiness–adult crime relationship withstood control for adolescent antisocial behavior. Self‐report sleepiness predicted to adult crime over and above objective measures of daytime sleepiness (EEG theta activity) and age 15 antisocial behavior. Poor daytime attention partly mediated the sleep–crime relationship. Mediation analyses also showed that social adversity predisposed to daytime sleepiness which was associated with reduced attention which in turn predisposed to adult crime. Conclusions Findings are the first to document a longitudinal association between sleepiness in adolescence and crime in adulthood. The longitudinal nature of this relationship, controlling for age 15 antisocial behavior, is consistent with the hypothesis that adolescent sleepiness predisposes to later antisociality. Findings are also consistent with the notion that the well‐established link between social adversity and adult crime is partly explained by sleepiness. Results suggest that a very brief and simple assessment of subjective daytime sleepiness may have prognostic clinical value, and that interventions to reduced sleepiness could be a useful avenue for future crime prevention.