Severe cash constraints faced by the Greek Government due to a pretty demanding schedule of interest and amortization payments in the remainder of 2015 have lately engineered a new explosion of sovereign bond spreads and rekindled fears of a GRexit down the road. Such fears have been exacerbated further in late April 2015 as the progress in implementing the February 20th 2015 Eurogroup agreement has proven to be rather slow and the cash-strapped Greek Government is struggling to meet sizeable debt service obligations. As a result, media reports had been speculating on a number of disastrous scenarios, ranging from the imposition of capital controls or the payment of civil servants and various state suppliers with promissory notes to a sovereign default, either within or outside the Economic and Monetary Union. This paper refrains from analyzing the legal and technical complications involved in the materialization of any of the aforementioned scenarios. Instead, it leans on purely economic and political economy considerations to argue that calls for exit are ill advised, potentially involving immense risks not only for Greece, but also for the EMU project as a whole. We take a close look at Greece’s past history of drachma devaluations and their outcome, the current high sovereign indebtedness, and the country’s persisting competitiveness gap vis-a-vis its main trading partners as well as the effects of financial contagion during the ongoing European Sovereign Debt Crisis. We explain why a GRexit would be a hugely suboptimal (and, in fact, a highly dangerous) strategy to address these problems.