Human Immunodeficiency Virus (HIV) infection is permanently established by integrating a deoxyribonucleic acid (DNA) copy into the human chromosome, a step also necessary to complete the Human Immunodeficiency Virus (HIV)replication cycle. Standard treatment of HIV infection suppresses Human Immunodeficiency Virus (HIV)replication and has not been able to eliminate Human Immunodeficiency Virus (HIV)from an infected person because of the integrated Human Immunodeficiency Virus (HIV). Raltegravir (RAL), the first approved antiretroviral (ARV) in a new class called integrase inhibitors, works by preventing integration of Human Immunodeficiency Virus (HIV). For participants with Human Immunodeficiency Virus (HIV)who have never taken antiretroviral medications, this research study will test whether Raltegravir (RAL), a recommended first-line ARV, can eliminate Human Immunodeficiency Virus (HIV)from key immune system cells.