In the last two years, Colombia and Chile have witnessed strong social protests, characterized by slogans against inequality and the lack of social mobility. In this study we propose a comparative study on social mobility and the persistence of structural social inequalities in both countries. We collect evidence on the level of social immobility and test if it is rooted in historical forms of social segregation in both countries. We base our analysis in surname based methods. We conclude that there are clear indications of a significant persistence of upward immobility of the groups that were originally segregated during the colonial period: Afro-descendants (Colombia) and indigenous people (in both). Furthermore, we find that the downward social immobility of the elites shows an important persistence in both countries. However, in Chile the colonial elites (encomenderos and landowners) present greater persistence in their privileged status, while in Colombia those early elites seem to have converged more quickly to the mean. In both countries, there is a clear persistence of the elites of the second half of the 19th century in todays highest position of the social ladder.