The question of how migration flows affect the labor markets of receiving countries has been widely debated by the economic literature but still lacks consensus, and rare are the studies addressing it in the context of high-skill migration. In addition, several Western countries adopted selective immigration policies to offset domestic skill shortages, while little evidence exists on their effectiveness. This paper aims to bridge both gaps by taking advantage of a French reform making it easier for firms to hire high-skill migrant workers in a specific set of occupations lacking native candidates. The analysis uses a rich set of administrative employer-employee data and relies on a difference-in-differences approach. Results show that the reform boosted migrants' hires without causing any harm to native employment, thus increasing the stock of labor in targeted jobs. In addition, entry wages of foreign workers decreased twice as much as the ones of natives, suggesting that the latter are in part shielded from the additional competition. Finally, the paper estimates the elasticity of substitution parameter recovered using the reform as an exogenous instrument and shows that immigrants and natives are imperfect substitutes in production, even when they are employed in the same occupations and by the same employer.