Countries have an incentive to use tariffs to gain advantage over trade partners, but an optimal tariff must weigh the benefits of an improved terms of trade against the costs that the tariff imposes on the domestic economy. In the presence of monopoly distortions and nominal rigidities, the stance of monetary policy may have a large effect on the evaluation of these costs. In a global economy where all countries set tariffs unilaterally in a 'trade war', the final outcome can differ dramatically depending on different monetary policy rules. We set out a model of a trade war in a New Keynesian open-economy model. For any one country, a tariff improves the terms of trade but is costly due to its deflationary effect on the domestic economy. A monetary rule which targets the CPI or stabilizes the nominal exchange rate exacerbates these latter costs, and leads to lower equilibrium tariff rates in a trade war equilibrium. Furthermore, an optimally delegated monetary rule can in fact completely eliminate a trade war.