Can public university Honors programs deliver the benefits of selective undergraduate education within otherwise nonselective institutions? We evaluate the impact of admission to the Honors College at Oregon State University, a large nonselective public university. Admission to the Honors College depends heavily on a numerical application score. Nonlinearities in admissions probabilities as a function of this score allow us to compare applicants with similar scores, but different admissions outcomes, via a fuzzy regression kink design. The first stage is strong, with take-up of Honors College programming closely following nonlinearities in admissions probabilities. To estimate the causal effect of Honors College admission on human capital formation, we use these nonlinearities in the admissions function as instruments, combined with course-section fixed effects to account for strategic course selection. Honors College admission increases course grades by 0.10 grade points on the 0 to 4 scale, or 0.14 standard deviations. Effects are concentrated at the top of the course grade distribution. However, course grades of first-generation students decrease in response to Honors admission, driven by low performance in natural science courses. Results suggest that selective Honors programs can accelerate skill acquisition for high-achieving students at public universities, but not all students benefit from Honors admission.