We investigate parental school choice in Berlin, Germany. Anecdotal evidence suggests that non-migrant "natives" take steps to avoid or seek out catchment area schools due to the ethnic composition of student bodies. Indeed, school segregation has been documented across Europe, but the lack of high-resolution data on school choice and migrant populations has made it difficult to precisely show the extent to which schools are more (or less) segregated than we would expect given catchment area demographics and to analyze the process that leads to such segregation. We contribute to this debate with an analysis of a never-before-used dataset of 35,000 school choice forms that parents must complete to enroll their child in elementary school. We combine this data with a newly compiled set of administrative data covering Berlin's several hundred elementary school enrollment zones for the years 2000 to 2018, which includes demographic and socioeconomic zone characteristics, student population indicators, and various school attributes and performance metrics. We explore in particular the extent to which we see Schelling sorting, where even weak preferences for separation from another group (and small changes in zone composition) can dynamically spiral to produce extreme patterns of segregation, and we develop policy implications for how to counteract such dynamics.