Over 90% of U.S. employers rely on hiring algorithms to screen job applicants. Many different employers use algorithms from the same few vendors. We conduct the largest empirical study of algorithmic hiring with data for 3.4 million real job applicants submitting 4 million applications to 156 employers across 11 market sectors. Every application was assessed by algorithms from a single vendor: we test whether this algorithmic monoculture bottlenecks job opportunities. We are the first to demonstrate large-scale evidence of racial disparities and homogeneous outcomes in high-stakes hiring decisions.