This thesis examines inequality of educational opportunities (IEO) in the transition to higher education. IEO measures the difference in higher education entry rates across social groups. The theoretical framework lays on Boudon's decomposition of IEO into primary and secondary effects of stratification. Furthermore, the theoretical propositions of Maximally Maintained Inequality (MMI) and Effectively Maintained Inequality (EMI) were also assessed to gain further understanding of IEO. The longitudinal data for the empirical analysis was created for a student cohort by linking administrative records of Chile's national student register, standardised tests and higher education enrolment. The student cohort was followed through the 12-years of compulsory education up to the transition to higher education, a year after completing secondary education. The results from the empirical analysis showed that secondary effects were consistently predominant over primary effects, driving the overall IEO. On the other hand, controlling for school characteristics increased the relative importance of secondary effects. However, primary effects explained a large extent of IEO in the transition to traditional (most prestigious) universities, by the same token, in the transition to undergraduate programmes. Differences in parental education levels between secondary education completion and higher education transitions proved to be consistent with MMI. Likewise, the higher likelihood of less advantaged students to enrol in vocational colleges or vocational programmes, and the higher likelihood of advantaged students to enrol in traditional universities or undergraduate programmes, evidenced support for EMI. The modelling setting was based on non-linear mediation modelling, accounting for sample-selection in the student cohort, two-level cross-classification between primary and secondary schools, and multinomial outcomes for type of institution and programme. This thesis contributes to the educational attainment literature by finding evidence that, in emerging economies like Chile, educational inequality persists despite the sustained expansion of the educational system.