In many countries, subsidies towards higher education and financial aid to students from poorer backgrounds have reduced socio-economic status (SES) gaps in undergraduate study. The increasing importance of graduate studies that are typically more expensive may, however, provide a new avenue for outcome differences by SES. We use administrative data from Ireland that allows us to take account of the exact undergraduate programme of study as well as a rich set of covariates. We find differences by SES in the probability of undertaking graduate study and larger differences in the type of programme entered. Low SES students are less likely to enter business/economic fields and more likely to enter education -- the lowest SES group enter fields with expected earnings that are, on average, about 3% lower compared to the highest SES group. We find that, at age 33, students in the lowest SES group who studied a graduate degree earn about 10% less compared to the highest SES group -- even for this high achieving group of graduates, those from the poorest backgrounds still earn significantly less than those from the most privileged backgrounds. Interestingly, we find choice of graduate programme can explain about 40% of this gap.