Central banks around the world have grappled with the question of how to respond to the mix of inflationary and output implications of a trade war. Recent tariff changes have impacted a wider cross-section of goods than was true in the previous tariff round, targeting final consumption goods in addition to materials such as aluminum and steel. This paper studies the optimal monetary stabilization of tariffs using a New Keynesian model enriched with comparative advantage between multiple traded sectors that differ in terms of tariff exposure as well as market structure and price rigidity. We find that, in the aggregate, the optimal monetary response is expansionary, supporting activity and producer prices at the cost of tolerating short-run headline inflation -- both in response to tariffs aimed at differentiated consumption goods and to tariffs on non-differentiated goods. The output and export dynamics arising from tariffs on each sector differ sharply, as do the motivations for an expansionary monetary response. Sectoral reallocation is an order of magnitude larger than predicted by standard macro models featuring one tradable and one nontradable sector.