This paper uses propensity score matching methods to investigate the relationship between breastfeeding and children's cognitive and noncognitive development. We find that breastfeeding for four weeks is positively and statistically significantly associated with higher cognitive test scores, by around one tenth of a standard deviation. The association between breastfeeding and noncognitive development is weaker, and is restricted to children of less educated mothers. We conclude that interventions which increase breastfeeding rates would improve not only children's health, but also their cognitive skills, and possibly also their noncognitive development.