In 2019-2020, the COVID-19 pandemic spread to over 200 countries in less than six months. To understand the basis of this aggressive spread, it is essential to determine the transmission rate and define the factors that increase the risk of transmission. One complication is the large fraction of asymptomatic cases, particularly in young populations: these individuals have viral loads indistinguishable from symptomatic people and do transmit the SARS-CoV-2 virus, but they often go undetected. As university students living in residence halls commonly share a small living space with roommates, some schools established regular, high density testing programs to mitigate on-campus spread. In this study, we analyzed longitudinal testing data of residence hall students at the University of Colorado Boulder. We observed that students in single rooms were infected at a lower rate than students in multiple occupancy rooms. However, this was not due to high rates of transmission between roommates, which only occurred approximately 20% of the time. Since these cases were usually asymptomatic at the time of diagnosis, this provides further evidence for asymptomatic transmission. Notably, individuals who likely transmitted to their roommates had an average viral load ~6.5 times higher than individuals who did not. Although students were moved to separate isolation rooms after diagnosis, there was no difference in time to isolation between these cases with or without transmission. This analysis argues that inter-roommate transmission occurs in a minority of cases in university residence halls and provides strong correlative evidence that viral load can be proportional to the probability of transmission.