We study optimal government debt maturity in a model where investors derive monetary services from holding riskless short-term securities. In a simple setting where the government is the only issuer of such riskless paper, it trades off the monetary premium associated with short-term debt against the refinancing risk implied by the need to roll over its debt more often. We then extend the model to allow private financial intermediaries to compete with the government in the provision of money-like claims. We argue that if there are negative externalities associated with private money creation, the government should tilt its issuance more towards short maturities. The idea is that the government may have a comparative advantage relative to the private sector in bearing refinancing risk, and hence should aim to partially crowd out the private sector's use of short-term debt.