Much research suggests that social networks affect individual and organizational success. However, a strong assumption underlying this research is that network structure is not reducible to the individual attributes of social actors. In this article, we test this assumption by examining whether interacting with random peers causes exogenous growth of a person's network. Using three years of network data for students at an Indian college, we evaluate the effect of peers on network growth. We find strong evidence that interacting with random, but well-connected, roommates causes significant growth of a focal student's network. Further, we find that this growth also implies an increase in how close an actor moves to a network's center and whether that actor is likely to serve as a network bridge. Fundamentally, our results demonstrate that exogenous factors beyond individual agency--i.e., random peers--can shape network structure. Our results also provide a useful model for causally identifying the determinants of network structure and dynamics.