This paper develops a model to study the macroeconomic implications of supply chain disruptions with three key ingredients: (i) a firm-level network of customized supplier-customer links that generate relationship-specific productivity gains; (ii) bargaining over these relationship-specific surpluses; and (iii) an extensive margin of adjustment, whereby firms decide to form or sever relations with suppliers and customers. We establish equilibrium existence and uniqueness, provide characterization results, and present a number of comparative statics that show how supply chains and aggregate output respond to shocks. We also show that equilibrium supply chains are inefficient and exhibit an inherent fragility: small shocks can lead to discontinuous changes in output, even though the efficient allocation is always continuous in the same shocks. We explore several macroeconomic implications of this fragility.