We develop an empirical approach to analyse, measure and decompose Inequality of Opportunity (IOp) in health, based on a latent class model. This addresses some of the limitations that affect earlier work in this literature concerning the definition of types, such as partial observability, the ad hoc selection of circumstances, the curse of dimensionality and unobserved type-specific heterogeneity that may lead to either upwardly or downwardly biased estimates of IOp. We apply the latent class approach to measure IOp in allostatic load, a composite measure of our biomarker data. Using data from Understanding Society (UKHLS), we find that a latent class model with three latent types best fits the data and that these types differ in terms of their observed circumstances. Decomposition analysis shows that about two-thirds of the total inequality in allostatic load can be attributed to the direct and indirect contribution of circumstances.