In a universal child care system with low or no parental co-payments, parents of advantaged socioeconomic backgrounds can improve the opportunities of their own children if they are better at identifying and occupying the high-quality centres, relegating children from disadvantaged backgrounds to centres of lower quality. To avoid such segregation, the generously publicly funded universal child care system in Norway is based on strict regulations of access, quality and co-payment. Still, using administrative data covering every child in Oslo over a decade, we document substantial segregation, with indications that children from advantaged families cluster in higher-quality centres. The segregation stems from parents of similar socioeconomic backgrounds applying to the same centres, and partly from private centres ‘cherry-picking’ advantaged children. Though parental application behaviour can to some extent be explained by residential segregation, we show that reallocating children across centres only 500 metres from their homes could substantially reduce segregation by immigrant background. We conclude that a child care system with almost universal participation and strict quality standards may not be sufficient to reduce social inequality and improve opportunities of disadvantaged children.