It seems well established that exposure to social stress, including acculturation stress, increases risk for psychiatric and substance problems, and that the disadvantaged experience higher levels of such exposure. Such evidence points to the expectation that immigrant minority groups must be at elevated risk relative to their native-born counterparts. That the opposite appears to be true for various immigrant groups within the U.S. constitutes what has been referred to as the nativity health paradox. This paper examines the association between nativity and drug dependence among the distinctive and understudied Hispanic population of South Florida and attempts to evaluate competing explanations for the apparent advantage of immigrant populations. Based on data on a representative sample young adults of Cuban and other Hispanic backgrounds (n=888), we found the paradox to be limited to women and confirmed the finding of prior research that acculturation plays a major role in explaining this difference in risk. We also found cumulative exposure to major and potentially traumatic events to be lower rather than higher among immigrants, to be a strong predictor of drug dependence and to contribute importantly toward accounting for observed nativity differences among women. Taken together, cumulative stress exposure and degree of acculturation explained 40% of the nativity difference. Finally, our results suggest that social support matters for risk primarily because such support more effectively acts to reduce exposure to social stress among foreign-born young Hispanic women.