In Switzerland, baccalaureate school is still considered to be the royal road to a university education and the elite path for the social reproduction of the upper class. However, cantonal enrollment to baccalaureate school varies widely due to Swiss federalism. There is a recurring debate on whether access to baccalaureate school is fair and equal among pupils who live in different cantons and who are of different social origin. This paper aims to analyze how the institutional conditions of cantons and municipalities impact a pupil's probability of entering baccalaureate school and how the cantonal provisioning of places in baccalaureate school affects social inequality of access. For our theoretical foundation, we combine concepts of neo-institutionalism with mechanisms of social reproduction in education. Empirically, we analyze national longitudinal register data to model educational transitions from compulsory to baccalaureate school by using logistic regression models. Our results show that institutional structures at the cantonal and municipal levels influence the probability of transition beyond individual pupils' characteristics. The degree of inequality varies between cantons, depending on the supply of baccalaureate school places. Inequality first increases with an increasing number of places (the scissors effect) and decreases only after the demand of more privileged families for places at baccalaureate school is saturated.