This paper provides a framework to study the macroeconomic implications of supply constraints. Supply constraints hamper firms’ ability to scale up production in response to surges in demand, disconnect prices from wages, and create non-linearities and instability in the aggregate Phillips curve. I use the model to show that binding supply constraints amplify the rise in inflation caused by a fiscal stimulus. This happens when the stimulus is large but transitory, when supply disruptions create shortages of intermediate inputs, and when public expenditure targets a few sectors of the economy. A persistent fiscal stimulus, instead, may boost firms’ investment and productivity growth in the medium run, while having only a transitory impact on inflation.