We uncover a puzzling link between low-frequency inflation and the population age-structure: the young and old (dependents) are inflationary whereas the working age population is disinflationary. The relationship is not spurious and holds for different specifications and controls in data from 22 advanced economies from 1955 to 2014. The age-structure effect is economically sizable, accounting eg for about 6.5 percentage points of US disinflation from 1975 to today's low inflation environment. It also accounts for much of inflation persistence, which challenges traditional narratives of trend inflation. The age-structure effect is forecastable and will increase inflationary pressures over the coming decades.