Safety and Immunotherapeutic Activity of an Anti-PD-1 Antibody (Cemiplimab) in Participants With HIV-1 on Suppressive cART

Inclusion Criteria: * HIV-1 infection * On ART for at least 24 months * Receiving ART with no changes of the components of ART medications within 90 days prior to study entry * Changes within drug class, in drug formulation or dose are allowed more than 30 days prior to study entry. * CD4+ T cell count ≥350 cells/mm\^3 * At least two plasma HIV-1 RNA less than the quantification limit of an FDA-approved assay within 18 months * A single detectable HIV-1 RNA but less than 1000 copies/mL is allowed if followed by HIV-1 RNA below quantifiable limits. * HIV-1 RNA level less than the quantification limit of an FDA-approved assay within 90 days prior to study entry * The following laboratory values within 90 days prior to entry: * Absolute neutrophil count (ANC) ≥1500 cells/mm\^3 * Hemoglobin ≥14.0 g/dL for men and ≥12.0 g/dL for women * Platelet count ≥150,000/mm\^3 * Creatinine clearance ≥60 mL/min * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) within normal limits * Normal thyroid, adrenal and diabetes testing * Negative tuberculosis (TB) test result, OR documentation of completed TB prophylaxis treatment * HCV antibody negative result or, if HCV antibody positive, undetectable HCV RNA result * Negative HBsAg result * Ability and willingness to provide informed consent. * Ability and willingness to continue non-study-provided cART throughout the study. * Female participants must have a negative pregnancy test. Agree not to participate in a conception process (e.g., active attempt to become pregnant or to impregnate, sperm donation, in vitro fertilization, egg donation) during the study. * When participating in sexual activity that could lead to pregnancy, agree to use at least two reliable forms of contraception simultaneously during the study through week 48. * Participants who are not of reproductive potential (women who have been post-menopausal for at least 24 consecutive months or have undergone hysterectomy and/or bilateral oophorectomy or salpingectomy or men who have documented azoospermia or undergone vasectomy) are eligible without requiring the use of contraceptives. * Weight ≥50 kg (110 pounds) Exclusion Criteria: * History of malignancy within the last 5 years. * Prior non-melanoma skin cancer (e.g., basal cell carcinoma or squamous cell skin cancer) is not exclusionary with documentation of complete resection at least 3 months prior to enrollment. * HIV-related opportunistic infections within the last 5 years * Chronic obstructive pulmonary disease (COPD). * Prior radiation therapy. * Active or previously treated active TB. * Active asthma requiring any treatment in the prior 2 years * Type I or type II diabetes mellitus. * History of or active autoimmune disorders including but not limited to inflammatory bowel diseases, scleroderma, severe psoriasis, myocarditis, uveitis, pneumonitis, systemic lupus erythematosus, rheumatoid arthritis, optic neuritis, myasthenia gravis, adrenal insufficiency, hypothyroidism and/or hyperthyroidism, autoimmune thyroiditis, hypophysitis, or sarcoidosis. * Immune deficiency other than that caused by HIV infection. * Currently breastfeeding or pregnant. * Known allergy/sensitivity or any hypersensitivity to mAb-based biologics, cemiplimab (anti-PD-1) or its formulation. * Active drug or alcohol use or dependence that, in the opinion of the site investigator, would interfere with adherence to study requirements. * Receipt of investigational drug or use of investigational medical device within 6 months prior to study entry. * Use of or intent to use immunomodulators (e.g., interleukins, interferons, cyclosporine, systemic corticosteroids exceeding physiologic doses), HIV vaccine, or systemic cytotoxic chemotherapy within 60 days prior to study entry. * NOTE: Participants receiving stable physiologic glucocorticoid doses, defined as prednisone ≤10 mg/day or the equivalent, will not be excluded. Stable physiologic glucocorticoid doses should not be discontinued for the duration of the study. In addition, participants receiving topical corticosteroids will not be excluded. * Any vaccination within 30 days * HCV treatment within 6 months * Prior immunoglobulin (IgG) therapy. * Current use or intent to use biotin ≥5 mg/day, including within dietary supplements. * History of chronic congestive heart failure or other significant cardiac conditions. * Any active, clinically significant medical condition that, in the opinion of the site investigator, would place the participant at increased risk.