Homelessness following eviction is a concerning problem in the United States. To mitigate this, local governments provide rental assistance programs to prevent at-risk individuals from entering into homelessness. Currently, however, such systems are reactive and do not prioritize those most at risk of homelessness, with individuals being prioritized manually. Our work with Allegheny County Department for Human Services (ACDHS) aims to more effectively and equitably allocate rental assistance through predictive modeling. Using historical data from ACDHS program enrollment, eviction courts, and more, we systematically predict entry into homelessness among all individuals with a recent eviction filing, significantly outperforming the current practice and several simple heuristic-based improvements.