Whether the nation’s most selective and resource-intensive colleges and universities serve as “engines of opportunity” rather than “bastions of privilege” depends on the extent to which they increase the educational attainment of students from the most economically disadvantaged backgrounds (Bowen, Kurzweil, and Tobin, 2005). Less than 11 percent of first-year students matriculating at 20 highly-selective institutions are from the bottom quartile of the income distribution, leading to significant concerns from higher education leaders and policy makers about the role of higher education in promoting intergenerational mobility. Recently, many elite public and private universities have introduced new initiatives designed to encourage the enrollment of low-income students. This paper assesses whether the population of low-income students with high observed academic achievement is sufficiently large that aggressive institutional policies could substantially increase the representation of low-income students at elite colleges. We use administrative data from the SAT and ACT to examine where students currently send scores (as a proxy for application) and assess whether differences in family income affect students’ choice sets. We also discuss how the effect of outreach and financial aid policies on outcomes is likely to differ appreciably across public and private institutions.