Postsecondary students increasingly enroll in online courses, which have the potential to further democratize higher education by expanding access for historically underserved populations. While a number of studies have investigated student outcomes in online courses, past data limitations have hindered robust examination of a potential mechanism underlying the decision to enroll in an online course: access to high speed broadband. With data from the National Broadband Map and IPEDS, I fit a number of Bayesian regression models to investigate the relationship between various measures of broadband access--download speed, upload speed, and the number of providers--and the number of students who take online courses at public colleges and universities with open admissions policies. Results show that increases in broadband speed at the lower end of the speed spectrum are positively associated with the number of students who take some of their courses online, but that the marginal gain diminishes as speeds increase. This finding suggests that there may be a minimum threshold of necessary broadband access, beyond which increases in speed become a less important factor in the take up of online coursework. Open admissions colleges seeking to improve access for local students through increased online course offerings should consider broadband access in the area, particularly if the targeted populations live in communities with low average broadband speeds.