The Eurozone debt crisis raises the issue of measuring and monitoring interconnected sovereign credit risk. We propose a novel empirical framework to assess the likelihood of joint and conditional failure for Euro Area sovereigns. Our model captures all the salient features of the data, including skewed and heavy-tailed changes in the price of CDS protection against sovereign default, as well as dynamic volatilities and correlations to ensure that failure dependence can increase in times of stress. We apply the model to Euro Area sovereign CDS spreads from 2008 to mid-2011. Our results reveal significant time-variation in risk dependence and considerable spill-over effects in the likelihood of sovereign failures. We further demonstrate the importance of capturing higher-order time-varying moments during times of crisis for the assessment of dependent risks.