This paper estimates the production function for early cognitive skill as a function of innate endowment, pre-natal influences, and post-natal influences. To disentangle the production technology from maternal preferences, we develop a model of maternal choice of child human-capital investment, consumption, labor, and leisure and study the properties of optimal choices. We take the model to data from the Infant Health and Development Program (IHDP), which recruited at birth 985 children born low-birth-weight and premature. Data on pre-natal care choices, made under the veil of ignorance with respect to child endowment, are used to proxy for maternal tastes. A treatment group was randomly assigned the offer of 1 year of weekly home visits followed by 2 years of free, full-day, high-quality care at a child development center. In our model, treatment constitutes a shock to the price and availability of high-quality care. Maternal responses with respect to parenting effort, maternal time use, and other margins are studied. We estimate parameters of the early cognitive skill production function with particular attention to the degree of productive complementarity between (1) pre-natal and age 0-3 investments (inter-temporal complementarity as in Cunha and Heckman, 2008) and (2) maternal and non-maternal post-natal care (intra-temporal complementarity as in the literature on the effects of maternal employment).