Carbon leakage and the relocation of firms is one of the main concerns of governments when choosing their climate policy. In a strategic trade model with endogenous plant location, we study the effect of border carbon adjustments (BCAs) on global welfare and emissions in an emission tax competition game between two asymmetric countries for two games: a simultaneous and a sequential game. Without BCAs, a ruinous “race to the bottom” with no relocation of firms is the only Nash equilibrium in a simultaneous game. In a sequential game, additionally, a “wise chicken” equilibrium may emerge where the Stackelberg leader gives in, letting all his/her plants relocate to avoid being stuck at the bottom. With BCAs, equilibrium emission taxes in both countries are higher, implying lower global emissions and usually higher global welfare in both games. With BCAs, the environmental more concerned country accepts that its firm partially relocates abroad, as it is rewarded with better control of global emissions, tariff revenues and higher net profits (profits minus taxes). This avoids high environmental damages and that either net profits are zero because of high subsidy levels in a “race to the bottom” or because all production plants have moved abroad.