This paper studies the influence of pre-migration social background on the long-term economic assimilation of immigrants. I use unique French survey data to trace family histories over three generations, before and after migration. While many immigrants experience an occupational downgrading at migration, their children benefit from various characteristics associated with the high socio-economic status their family had in the origin country. As a result, characteristics of immigrant grandparents are highly predictive of their grandchildren's educational attainment.