We study the liquidity choice of a bank subject to rollover risk and support from a lender of last resort (LLR) and study the consequences for bank stability, funding costs, and liquidity regulation. The liquidity choice balances forgoing profitable yet illiquid investment with fewer panic runs and cheaper debt. A higher LLR penalty rate increases bank liquidity and has a V-shaped effect on ex-ante bank stability. Turning to normative implications, the availability of the LLR reduces welfare for a large social cost of bank failure. The anticipation of ex-post support mitigates panic runs but induces lower bank liquidity ex ante, which increases funding costs and the frequency of bank failure. Liquidity regulation aligns private with social incentives and increases the social value of LLR support.