The massive accumulation of international reserves in developing economies is a puzzling recent development in the world economy. This paper studies reserve accumulation as the outcome of a simple model in which the central bank smooths inflation. I explore the view that central banks accumulate reserves to face large fiscal shocks that need monetary financing. Central bank revenues are obtained through inflation, but inflation is distortionary. As a result, the central bank optimally accumulates international reserves in order to spread the costs associated with inflation over time. A simple numerical exercise for an average developing economy using data between 1970 and 2009 yields fast growth of international reserves.