This paper measures the pass-through of exchange rate changes into domestic inflation within a cointegrated VAR (CVAR) framework. This issue is of particular interest for the euro area (EA) as Member Sates cede their national currencies and no longer have options of using monetary policy to respond to local conditions. In fact, a common exchange rate shock, in the absence of a national monetary policy, may have differential impact on EA countries, leading notably to possible divergence in inflation levels. Using quarterly data for 12 EA covering 1980:1 to 2010:4, we report a large degree of heterogeneity in the rates of pass-through across our sample, especially, between "peripheral" and "core" EA economies. For instance, prices rise by 84% in Portugal following one percent depreciation of exchange rate, while for the German economy the extent of pass-through is not exceeding 0.20%. This outcome would have important implications for the general risk perceived by foreign firms and investors regarding the inflationary environment within each EA country.