We study the effects on inequality of a "Piketty transition" to zero growth. In a model with a worker-capitalist dichotomy, we show first that the relationship between inequality (measured as a ratio of incomes for the two types) and growth is complicated; zero growth can raise or lower inequality, depending on parameters. Extending our model to include idiosyncratic wage risk we show that growth has quantitatively negligible effects on inequality, and the effect is negative. Finally, following Piketty’s thought experiment, we study how the transition might occur without declining returns; here, we find inequality decreases substantially if financial innovation acts to reduce idiosyncratic return risk, and does not change much at all if it acts to increase capital’s share of income.