Unraveling, the excessively early matching of future workers to employers, is a pervasive phenomenon in entry-level labor markets that leads to hiring decisions based on severely incomplete information. We provide a model of unraveling in one-to-one matching markets for prestigious positions. Its distinguishing feature is that the market operates over an extended time period during which information about potential matches arrives gradually. We find that unraveling causes potentially thick markets to spread thinly over a long time period. In equilibrium, an employers desirability is correlated neither with the time at which they hire, nor with the expected productivity of their matched worker. Unraveling thus significantly redistributes welfare among employers compared to a pairwise stable match. We study policies that manipulate the availability of information about students and show that they are effective only if they provide a sudden surge in information. Our main application is the market for U.S. federal appellate court clerks, a significant input into the efficiency of the justice system. Consistent with the model, hiring times in our dataset are spread over a period of six months and are uncorrelated with the desirability of a judge as an employer.