Immigrants are underrepresented in most democratic parliaments. To explain the immigrant-native representation gap, existing research emphasizes party gatekeepers and structural conditions. But a more complete account must consider the possibility that the representation gap begins at the supply stage. Are immigrants simply less interested in elected office? To test this explanation, we carried out an innovative case-control survey in Sweden. We surveyed elected politicians, candidates for local office, and residents who have not run; stratified these samples by immigrant status; and linked all respondents to local political opportunity structures. We find that differences in political ambition, interest, and efficacy do not help explain immigrants' underrepresentation. Instead, the major hurdles lie in securing a candidate nomination and being placed on an electable list position. We conclude that there is a sufficient supply of potential immigrant candidates, but immigrants' ambition is thwarted by political elites.