A Single Dose of Pembrolizumab in HIV-Infected People

Background: Human immunodeficiency virus (HIV) attacks the immune system. Some people with HIV have a low CD4+ T-cell count despite taking antiviral medicines that control HIV replication. These cells fight disease, so a low count makes it easier for people to become sick. Researchers want to see if a new drug can improve the immune system, including T cells. The drug is called pembrolizumab Objective: To see if pembrolizumab is safe to use in people with HIV who have a low CD4+ T cell count despite taking medicines that control HIV replication, and to see if it strengthens the immune system. Eligibility: People age 18 years or older with HIV who are taking antiretroviral drugs as treatment, have blood HIV levels below detection limits of commercial assays, and have a low CD4+ T-cell count (below 350 cells/mm3). Design: Participants will be screened with: * Medical history * Physical exam * Heart, blood, and urine tests Sexually active participants must use 2 kinds of birth control. Participants will have leukapheresis. Blood will be removed through a needle in one arm. A machine will remove white blood cells. The rest of the blood will be returned into the other arm. Participants will have a baseline visit. They will have blood tests. They may have a pregnancy test. A needle will insert a thin plastic tube (IV) into an arm vein. The participants will get the study drug or a placebo through the IV for 30 minutes. They will be watched for a couple hours after. Participants will have 11 follow-up visits over the next 48 weeks. They will have a physical exam, vital signs, medical review, and blood tests. Participants may have another leukapheresis. Participants will be called every 12 weeks after their last follow-up visit to talk about how they feel and their health. Participation ends after the week 96 phone call.