Created in 1965, the federal Head Start program is among the more prominent educational initiatives in the US. By giving matching grants to programs providing comprehensive early education, health care, and nutritional services to poor children, and parenting training to their parents, Head Start aims to raise educational attainment levels and narrow educational inequalities. Head Start now enrolls more than 900,000 children. In 1998, Congress mandated a national evaluation of Head Start. The resulting Head Start Impact Study (HSIS) is a randomized control trial designed to determine the impact of Head Start on children's school readiness and parental practices. We use these experimental data to test the two distributional hypotheses we lay out below. One hypothesis is that the effects of Head Start availability will vary across the skill distribution, with students at the bottom of the distribution of skill experiencing the most pronounced positive academic and language effects. Similarly, if this hypothesis is correct, we expect the program to improve the behavior of children who are relatively prone to behavior problems. In contrast, the ``skills-begets-skills'' hypothesis suggests that the positive effects of Head Start may be concentrated at the top of the skill distribution. It is not implausible that students who have basic language and numeric competencies are more able to participate fully in the Head Start curriculum than their academically or developmentally-delayed peers. We use recently released data from the Head Start Impact Study and quantile treatment effects to identify the impact of assignment to an offer of Head Start placement on the distribution of child outcomes. The HSIS study randomized children applying to oversubscribed Head Start centers for the first time to either an offer of a slot or denial of a slot for one year. These data follow cohorts of 3- and 4-year old children through first grade, collecting detailed outcomes on academic and social-emotional measures. Preliminary evidence suggests a positive effect of assignment of an offer of Head Start on achievement scores at the bottom of the distribution.