New York City's "Pre-K for All" (PKA) is the Nation's largest universal early childhood initiative, currently serving some 70,000 four-year-olds. Stemming from the program's choice architecture as well as the City's stark residential segregation, PKA programs are extremely segregated by child race/ethnicity. Our current study explores the complex forces that influence this segregation, including the interplay between family choices, seat availability, site-level enrollment priorities, and the PKA algorithm that weighs these and other considerations. We find that a majority of PKA segregation lies within rather than between local communities, suggesting that reducing segregation would not necessarily require families to choose programs far from home. On a more troubling note, areas with increased options and greater racial/ethnic diversity also exhibit the most extreme segregation.