Study Overview: This research is about using a drug called baricitinib to reduce HIV in the central nervous system (CNS). HIV is a virus that affects the immune system, and while current treatments can control it, they can't cure it. Baricitinib is a medicine usually used for arthritis, but it might help reduce HIV in the brain, where the virus hides. The study will compare baricitinib to a placebo, which is a harmless pill that doesn't contain the drug. Participants will undergo tests like bloodwork, brain scans, and memory tests to see if baricitinib is effective.

• The study involves several visits and tests like MRIs, blood tests, and memory exams.
• Participants must be adults with controlled HIV on ART and not have serious health issues like heart disease or liver problems.
• Women must not be pregnant and should agree to use birth control during the study.

Eligibility: To join, you must be 18-65 years old, on HIV treatment with stable health, and agree to follow study guidelines. You cannot join if you are pregnant, have certain infections or diseases, or have recently had major surgery.