I study how growth, via structural transformation, affects volatility. Growth in the United States has led to a shift in resources from agriculture and manufacturing to services. Since the service sector is the least volatile, this shift can potentially reduce aggregate volatility. Existing studies have explored this idea by aggregating sectoral volatilities to the economy-wide volatility when the sector shares are independent of sectoral shocks. But theories of structural transformation highlight the strong links between these: sectoral shocks are the source of changes in sectoral shares. I incorporate this relationship by developing a fully specified dynamic model of structural transformation with real business cycles, and use it to derive the equilibrium relationship between sectoral and aggregate volatilities. I then feed into my model the measured sectoral volatilities and growth trends. I find that growth, via structural transformation, can account for one third of the reduction in the volatility of US GDP in 1984-2007 compared to 1947-1983. This contrasts existing work that suggests that aggregate volatility is largely influenced by sectoral composition.