We use the natural experiment of a state lottery scholarship to measure the effect of generous financial aid on graduation rates at New Mexico's flagship public university. During the study period, the scholarship program paid full tuition for eight semesters for any state resident earning a 2.5 grade point average in their first semester at any public two-year or four-year college. We find a significant positive completion effect of 10 percentage points (17.9 percent) for academically well-prepared students that is offset by a large negative effect of 11.6 percentage points (38.8 percent) for less-prepared students. We posit that the scholarship program, which effectively erased the difference in tuition at two- and four-year colleges, may have induced weaker students to take their chances on a more prestigious, yet riskier, academic path.