Background: Efforts to improve the U.S. public education system have, in recent decades, focused on strengthening the quality of the teacher workforce, given the large body of evidence documenting teachers' central role in shaping student outcomes (e.g., Chetty et al. 2014; Kane & Staiger 2008; Rockoff 2004). Much research has examined efforts to improve teachers' performance on the job through professional development, performance-evaluation systems, and merit pay (e.g., Adnot & Wyckoff 2015; Jackson et al. 2014; Authors 2020). And, economists have argued for policies that replace ineffective teachers with more-effective teachers (Gordon et al. 2006; Hanushek 2011; Staiger & Rockoff 2010). However, we know far less about the potential to strengthen the teacher workforce through a critical step in the human capital pipeline: teacher hiring. Theoretical models from the personnel economics literature suggest that inefficient hiring in the public education sector may inhibit potential gains to teacher quality (e.g., Oyer & Schaffer, 2011). But, hiring remains a relatively understudied part of the process of improving human capital in schools. Research Questions: In this paper, we explore how labor supply and the temporal dynamics of the hiring process are related to the quality of newly hired teachers. The potential to improve teacher quality through the hiring process depends critically on how local teacher supply evolves over the course of a hiring period and differs across positions and schools. Job candidates enter and exit the market as schools compete against each other to make offers and attract candidates. Given the distinctly seasonal nature of teacher hiring, applicant quantity and quality decline over time. Thus, competitive search models suggest that earlier hiring timelines can reap substantial benefits for school systems. Public-school teachers in large urban districts are frequently hired late in the summer or even after the school year starts, to the detriment of their students (Engel 2012; Levin & Quinn 2003; Liu & Johnson 2006; Authors 2016). Early hiring should afford early-acting schools the advantage not only of a larger applicant pool, but also the opportunity to move quickly to attract their top candidates (Mortensen & Pissarides 1999; Oyer & Schaefer 2011; Rogerson et al. 2005). Data, Setting, and Methods: We explore these theoretical predictions using detailed hiring records from 129 schools in the Boston Public School district (BPS). BPS provides an advantageous context for exploring these questions. Unlike most public-school systems, BPS gives individual schools substantial staffing autonomy. BPS also follows an open posting process that allows all schools to start hiring--and all candidates to begin applying--well before most districts publicly post openings. BPS effectively operates as an unconstrained open market, allowing us to observe local labor supply dynamics as schools compete for teacher candidates within a local market. We begin our analysis by exploring the extent to which supply varies across types of positions (i.e., by subject area). We next examine the degree to which supply differs across schools, decomposing the variance in supply attributable to individual schools within specific position types; we additionally estimate models of school value added to supply. We then explore the temporal dynamics of teacher hiring, across and conditional on the features of the position, documenting cumulative patterns of movement into and out of the BPS market over time. Specifically, we document trends in the volume of both supply (the size of the active applicant pool) and demand (number of new job postings) over the course of the hiring window. Finally, we examine the consequences of these factors for the quality of a school's new hire estimating regression models that control for features of the position, broader labor supply dynamics, and the school itself. Hiring outcomes include effects on student achievement, classroom observation scores, retention, diversity, and qualifications. We build our models incrementally to demonstrate the separate and conditional associations between timing and supply on hiring quality. Findings: We find multiple distinct teacher labor markets at play within BPS, with different implications for hiring across positions and schools. On the supply side, the volume of applicants varies widely across subjects and over the course of the hiring season. Local supply also differs meaningfully across individual schools--even for similar positions posted on the same dates--reflecting both applicant preferences and hiring actions within the school. Overall, BPS has a large potential applicant pool, yet schools that post later miss out. Teachers enter the market early when given the opportunity; half of all applicants begin applying in the first seven weeks of the hiring window. Meanwhile, more than one in six positions have yet to be posted on July 1, the date by which BPS aims to complete its hiring, and by which point a majority of applicants have already effectively exited the market. Crucially, more-effective candidates begin and cease applying to positions earlier, suggesting real benefits from accelerating hiring timelines. Finally, while earlier postings receive more applicants and are more likely to be filled, the size of the applicant pool conditional on timing is largely unassociated with the effectiveness of the hire. Schools that recruit large applicant pools are more likely to hire candidates who are more attractive based on paper credentials, such as certification, but no more likely to select candidates who are more effective in the classroom or who are more likely to remain at the school (indicative of a positive teacher-school match). These patterns suggest that schools struggle to identify and select the best candidates even in the face of a large supply of applicants (e.g., Jacob et al. 2018). Conclusion: These findings imply that schools are not fully realizing the potential gains of expanded applicant pools through early hiring, nor are they leveraging larger pools to attract more qualified candidates. Even the schools that post early and elicit large volumes of applicants are, on average, staffing their schools with new hires who are not consistently better than those at schools hiring from more constrained applicant pools. Ultimately, while timing is important, its advantages may not be fully realized unless schools can screen effectively.