Nominal rigidities due to menu costs have become a standard element in closed economy macroeconomic modeling. The "New Open Economy Macroeconomics" literature has investigated the implications of nominal rigidities in an open economy context and found that the currency in which prices are set has significant macroeconomic and policy implications. In this paper we solve for the optimal invoicing choice by integrating this microeconomic decision at the firm level into a general equilibrium open economy model. Strategic interactions between firms play a critical role in the analysis. We find that the less competition firms face in foreign markets, as reflected in market share and product differentiation, the more likely they will price in their own currency. We also show that when a set of countries forms a monetary union, the new currency is likely to be used more extensively in trade than the sum of the currencies it replaces.