What is the effect of Central Bank Digital Currency (CBDC) on financial stability? We answer this question by studying a model of financial intermediation with an endogenously determined probability of a bank run, using global games. As an alternative to bank deposits, consumers can also store their wealth in remunerated CBDC issued by the central bank. Consistent with widespread concerns among policymakers, higher CBDC remuneration increases the withdrawal incentives of consumers, and thus bank fragility. However, the bank optimally responds to the additional competition by offering better deposit rates to retain funding, which reduces fragility. Thus, the overall relationship between CBDC remuneration and bank fragility is U-shaped.