This paper considers the impact of Programa de Educación, Salud y Alimentación (PROGRESA), a large Mexican rural anti-poverty programme that had an evaluation sample in which overall treatment was randomly assigned to some communities but not others, on child nutrition. When we examine the impact of PROGRESA based on the presumption of randomized allocations, we find that PROGRESA had no or even a negative impact on child nutrition. However, not all children designated to receive nutritional supplements actually did so. Our preferred estimates – child fixed-effects estimates that control for unobserved heterogeneity that is correlated with access to the supplement – indicate a significantly positive and fairly substantial programme effect of the nutritional supplements on children 12–36 months. They imply an increase of about a sixth in mean growth per year for these children and a lower probability of stunting. Effects are somewhat larger for children from poorer communities but whose mothers are functionally literate. The long-term consequences of these improvements are non-trivial; its impact working through adult height alone could result in a 2.9% increase in lifetime earnings.