We estimate the systemic effects of exit by a key over-the-counter (OTC) intermediary. In our model, risk-averse traders are connected by a core-periphery network. If traders are also averse to concentrated bilateral exposures then the incomplete network prevents full risk-sharing. We quantify the impact of the network structure on prices using the closed-form solution to our model and proprietary data on all credit default swap (CDS) transactions in the U.S. from 2010-2013. There are a small number of key OTC intermediaries whose exit can move markets dramatically. Eliminating one of these leads credit spreads to increase over 20%.