A prominent solution to the time-inconsistency problem inherent to monetary policymaking consists of delegating monetary policy to an independent central bank by an appropriately designed inflation contract or target. This paper shows that delegation is not a solution to this problem: optimal delegation requires commitment and is not time-consistent, while time-consistent delegation is suboptimal. We prove these results formally in a popular dynamic model of monetary policy. Introducing costs of reappointing the central banker can only solve this problem if the government is infinitely averse to changing central bank’s contract.