The recent growth in the number and diversity of schools around the world classified as "International Schools" raises questions about what makes a school's claim to be an International School legitimate. From the analysis we report here, the provision of an international curriculum emerges as what a school must do to be legitimate as an International School. It is an International School's primary task and those in such a school ideally undertake institutional work on that task. We consequently bring the idea of the institutional primary task into institutionalisation theory where it assumes a significant but previously unacknowledged place and a key consideration in institutional legitimacy. In the article, we use the provision of the International Baccalaureate Diploma Programme in an International School to illustrate the notions of the institutional primary task and the pillars and carriers of institutionalisation in practice. The analyses reported in the article develop understandings of International Schools and institutionalisation theory.