By exploiting a commuting policy that led to a sharp and unexpected inflow of Czech workers to areas along the German-Czech border, we examine the impact of an exogenous immigration-induced labor supply shock on local wages and employment of natives. On average, the supply shock leads to a moderate decline in local native wages and a sharp decline in local native employment. These average effects mask considerable heterogeneity across groups: while younger natives experience larger wage effects, employment responses are particularly pronounced for older natives. This pattern is inconsistent with standard models of immigration but can be accounted for by a model that allows for a larger labor supply elasticity or a higher degree of wage rigidity for older than for young workers. We further show that the employment response is almost entirely driven by diminished inflows of natives into work rather than outflows into other areas or non-employment, suggesting that "outsiders" shield "insiders" from the increased competition.