Baricitinib Curative Repression of HIV-1

Inclusion Criteria: * Documented HIV infection * On continuous ART for at least 96 weeks before enrollment, with no interruption of ART for 7 consecutive days or longer in the 48 weeks before enrollment. * Plasma HIV-1 RNA levels of \<50 copies/mL for at least 96 weeks (a minimum of two measures), and \<50 copies/mL for a sample obtained within 90 days, before enrollment. * CD4+ T-cell count ≥500 cells/mm3 obtained within 90 days prior to enrollment * No known history of CD4+ T-cell count nadir \<200 cells/mm3 * Negative pregnancy test at time of study enrollment * Additional laboratory criteria may apply. Exclusion Criteria: * \< 18 years of age or \> 70 years of age * Pregnancy or breastfeeding, as determined by a blood pregnancy test * History of AIDS-defining illness, except for recurrent pneumonia. * History of progressive multifocal leukoencephalopathy or clinically significant HIV-associated neurocognitive disease. * Untreated latent tuberculosis infection (which will be screened for before entry). If there is a prior positive test, the test does not need to be repeated at screening. * History of use of any immunomodulatory medications within 6 months before enrollment, including systemic corticosteroids (\>14 days), immunosuppressants, anti-cancer, interleukins, systemic interferons, systemic chemotherapy, or other medications that the site investigator feels could have an immunomodulatory effect. * History of deep venous thrombosis * Cardiovascular disease (Coronary artery disease or history of myocardial infarction, Congestive heart failure with left ventricular ejection fraction ≤40% per American Heart Association guidelines, history of stroke) * History of HIV-associated malignancy, including Kaposi's sarcoma, or any lymphoma/leukemia or virus-associated cancers. Active or recent non-HIV-associated malignancy requiring systemic chemotherapy or surgery in the preceding 36 months * Major surgery within 8 weeks before screening, or will require major surgery during the study * Current or recent (\<4 weeks before screening) clinically serious viral (including COVID-19), bacterial, fungal, or parasitic infection or any other active or recent infection. History of untreated syphilis infection. If a rapid plasma reagin (RPR) test was negative in the 3 months before screening, then an RPR is not needed at screening * Symptomatic herpes simplex at the time of screening. * Symptomatic herpes zoster infection within 12 weeks before screening. * History of disseminated/complicated herpes zoster (for example, ophthalmic zoster or central nervous system (CNS) involvement). * Positive test for hepatitis B virus (HBV) * Additional exclusion criteria apply