Two landmark policy interventions to improve the lives of youth through neighborhood, the Gautreaux program in Chicago and the Moving to Opportunity (MTO) experiments in five cities, have produced conflicting results and have created a puzzle with broad implications: Do residential moves between neighborhoods increase or decrease violence, or both? To address this question, we analyze data from a subsample of adolescents' ages 9-12 years from the Project on Human Development in Chicago Neighborhoods, a longitudinal study of children and their families that began in Chicago, the site of the original Gautreaux program and one of the MTO experiments. The authors propose a dynamic modeling strategy to separate the effects of residential moving across three waves of the study from dimensions of neighborhood change and metropolitan location. The results reveal countervailing effects of mobility on trajectories of violence; whereas neighborhood moves within Chicago lead to an increased risk of violence, moves outside the city reduce violent offending and exposure to violence. The gap in violence between movers within and outside Chicago is explained not only by the racial and economic composition of the destination neighborhoods but also by the quality of school contexts, adolescents' perceived control over their new environment, and fear. These findings highlight the need to simultaneously consider residential mobility, mechanisms of neighborhood change, and the wider geography of structural opportunity. Tables, references, and appendix (Published Abstract)