Gero Hütter and co-authors reported the first long-term remission or "cure" of HIV/AIDS in a human. The patient, Timothy Ray Brown also known as "The Berlin Patient" also suffered from myeloid leukemia and underwent stem-cell transplanation (bone marrow transplant) as treatment for his leukemia. The stem-cell donor lacked the CCR5 HIV virus receptor on his cells. When these cells were transplanted into the "The Berlin Patient" the donor's cells totally replaced the patient's bone marrow cells with cells that lacked the CCR5 HIV virus receptor and made the recipient "immune" to HIV. Thus "The Berlin Patient" was "cured" of both AIDS and leukemia. Digital edition of this paper from nejm.org at this link.
The first replication of cure of HIV/AIDS by this method was accomplished 10 years later in March 2019 by a team lead by Ravindra Gupta: "HIV-1 remission following CCR5Δ32/Δ32 haematopoietic stem-cell transplantation," Nature, 568, 244–248 (2019).
(Thanks to Juan Weiss for this addition to the bibliography.)