In this paper, we consider how monetary policy in a large, foreign economy affects optimal monetary policy in a small open economy (`home') in response to a large global demand shock that pushes both economies to the zero lower bound (ZLB) on nominal interest rates. We show that the inability of foreign monetary policy to stabilise the foreign economy at the ZLB creates a spillover that affects how well the home policymaker is able to stabilise its own economy. We show that more stimulatory foreign policy worsens the home policymaker's trade-off between stabilising inflation and the output gap when home and foreign goods are close substitutes. This reflects the fact that looser foreign policy leads to a relatively more appreciated home real exchange rate, which induces large expenditure switching away from home goods when goods are highly substitutable--just at a time (at the ZLB) when home policy is trying to boost demand for home goods. When goods are not close substitutes, the home policymaker's ability to stabilise the economy benefits from more stimulatory foreign policy.