This paper develops a model of tax competition with three countries that initially form a union where countries refrain from using different tax rates in different sectors of the economy. We study the impact of one country leaving the union. We show that the introduction of discriminatory taxation in one country increases tax policy heterogeneity within the remaining union. Moreover, the incentives for the two remaining countries to harmonize their tax rates decline. We discuss these results in the context of the debate on the tax policy implications of Brexit.