Housing Our Heroes Act This bill directs the Department of Veterans Affairs (VA) to begin a three-year pilot grant program to assess the feasibility of awarding grants to eligible entities to purchase and renovate abandoned homes for homeless veterans. Eligible entities are veterans service agencies and organizations, homeless organizations, and other nongovernmental organizations that demonstrate a record of financial stability and experience in developing housing for homeless veterans. The VA shall give grant priority to entities that serve communities with the greatest need of homeless services and may give grant priority to achieve geographic grant distribution. The bill establishes the Veterans Homelessness Grant Fund.