Services for Ending Long-Term Homelessness Act This bill amends the Public Health Service Act to require the Substance Abuse and Mental Health Services Administration to design national strategies and implement programs to address chronic homelessness. To promote an end to chronic homelessness, the Department of Health and Human Services must award grants to provide: mental health services; substance use disorder treatment; integrated, coordinated treatment for co-occurring disorders; health education; services designed to help individuals and families make progress toward self-sufficiency; and other supportive services that promote an end to chronic homelessness. Priority for grants is given to applicants that target services to individuals and families who have experienced more homelessness, use more public emergency care, or have a history with the criminal justice system.