This paper analyzes the optimal allocation of losses via a Central Clearing Counterparty (CCP) in the presence of counterparty risk. A CCP can hedge this risk by providing loss-absorbing capital or by mutualizing losses among its members. This protection, however, weakens members' incentives for risk management. Delegating members' risk monitoring to the CCP alleviates this tension in large markets. To discipline the CCP at minimum cost, members oer the CCP a junior tranche and demand capital contribution. Our results thus endogenize the default waterfall and deliver novel predictions on its composition, collateral requirements, and CCP ownership structure.