Central banks create money to lend during credit crunches, which might lead to inflation. We examine whether the two key functions of central banks—price stability and last-resort lending—conflict. We develop a nominal model of bank runs à la Diamond and Dybvig (1983) in which individuals can store the money they withdraw “under the mattress” or use it to buy assets. This feature allows for lending of last resort without creating inflation. Our analysis also provides a new rationale for the “Bagehot rule”: High interest rates prevent inflation, rather than mitigate the risk of lending during credit crunches.