We propose a model of the financial system in which banks are individually prone to runs and connected through fire sales. Strategic complementarities within and across banks amplify each other, making heterogeneity in bank risks a key factor shaping the fragility of each bank and the entire system. As long as different banks are interconnected, an increase in heterogeneity stabilizes all banks. Reductions in asset commonality, bank-specific disclosures, and even broad-based policies such as asset purchases and liquidity requirements can enhance stability by increasing bank heterogeneity.