Broadly Neutralizing Antibodies 3BNC117-LS & 10-1074-LS to Prevent Relapse During ATI

Participants will receive an infusion of both study drugs (3BNC117-LS and 10-1074-LS) and will discontinue antiretroviral therapy (which is the treatment for HIV) two days later. Participants will receive a second dose of the first study drug (3BNC117-LS) at week 12 if the HIV infection is maintained and participants remain off of antiretroviral therapy. The study hypothesizes that intravenous infusions (which means medication is delivered directly into a participant's vein) of the combination of study drugs will be safe and well tolerated, will maintain control of the HIV infection without antiretroviral therapy, and may be associated with a decrease in HIV found in cells that were previously infected with HIV but not actively producing HIV in the body.