It is well-established that neonatal health is a strong predictor of socioeconomic outcomes later in life, but does neonatal health also predict key outcomes of the next generation? This paper documents a surprisingly strong relationship between birth weight of parents and school test scores of their children. The association between maternal birth weight and child test scores corresponds to 50-80 percent of the association between the child's own birth weight and test scores across various empirical specifications, for example including grandmother fixed effects that isolate within-family differences between mothers. Paternal and maternal birth weights are equally important in predicting child test scores. Our intergenerational results suggest that inequality in neonatal health is important for inequality in key outcomes of the next generation.