We explore the dynamics of competitive search in the K-12 public education sector. Using detailed panel data on teacher hiring from Boston Public Schools, we document how teacher labor supply varies substantially across vacancies even within a single district depending on position type, school characteristics, and the timing of job postings. We find that early-posted positions are more likely to be filled and end up securing new hires that are better qualified, more effective, and more likely to remain at a school. In contrast, the number of applicants to a position is largely unassociated with hire quality, suggesting that schools may struggle to identify and select the best candidates even when there is a large pool of qualified applicants. These patterns persist even when we restrict comparisons to only positions within an individual school using school fixed effects. Our findings point to substantial unrealized potential for improving teacher hiring.