This paper studies the relation between seigniorage and inflation in Argentina for the period 1979-1989. We estimate a money demand function and derive the Laffer curve for several sub-periods with different monetary/exchange rate regimes. We find that for most of the period the Argentine economy remained on the efficient" side of the Laffer curve. The long-run revenue maximizing rate of inflation has been around 20% per month for the "tablita" (1979-1981) and post-Austral (1985-1988) periods and around 30% per month for the pre-Austral period (1982-1985). The long-run maximum level of seigniorage has been above 6% of GDP. Our results imply that the hyperinflation experienced by Argentina in 1989 can be interpreted as an unstable phenomenon that resulted from the need to collect a level of seigniorage that exceeded the maximum warranted by the demand for money.