There is good evidence that children of parents with alcohol problems have more drug involvement, plus related mental health and behavioral problems. In this study, we sought to estimate the degree to which these children might be more likely to initiate drug use precociously. A sample of 2888 parent-child pairs was identified within public data files of the National Household Survey on Drug Abuse (NHSDA), 1995-1997. Alcohol dependence of one parent was assessed by that parent's report of three or more dependence manifestations. Independently, one randomly selected 12-17 year-old child of the parent answered self-report survey questions on age at first use of tobacco, alcohol, and marijuana. In analyses contrasting 114 children of alcohol dependent parents (AD+) with 2774 other children (AD-), youths with alcohol dependent parents had higher odds than other kids to have used tobacco in the past year (odds ratio, OR=3.2, 95% confidence interval, CI=2.05-4.98), as well as alcohol (OR=1.6, 95% CI=1.05-2.50), and marijuana (OR=2.9, 95% CI=1.71-4.90). Survival analyses were used to clarify excess risk of early-onset drug use. For example, by age 17, an estimated 73% of AD+ children had smoked tobacco cigarettes, 70% had started drinking, and 41% had smoked marijuana, versus 44%, 57%, and 26% of AD- children, respectively. This new evidence helps build a case that children of parents with alcohol problems experience precocious drug use.