The rise of digital currencies may result in domestic parallel currencies. Their exchange rate shocks will present a new challenge for monetary policy. We analyze these issues in a New Keynesian framework, where rms can set prices in one of the available currencies. Price rigidity translates a one-time appreciation of a parallel currency into persistent redistribution towards the dollar sector output and inflation. The persistence lasts longer if the central bank targets “dollar”-sector inflation, rather than inflation across all currency sectors. An increase in dollar price rigidity may lead to a decrease rather than an increase of the non-dollar sector.