The procedure will involve taking cells from the marrow of a baboon and injecting them into the patient, Jeff Getty, a 38-year-old Aids activist from San Francisco.
Doctors have estimated that Mr Getty has less than a year to live. The hope is that the baboon's cells, which have undergone treatment to reduce the risk of rejection by the human body, will provide the immune response necessary to save the patient's life.
The government's Food and Drug Administration blocked the experiment earlier this year, noting that not enough was known yet about the risks of cross-species transplants, known as xeno-transplantations. Aids is believed to have evolved from a virus that first infected other species.
Some members of the FDA panel that met on Friday remarked that they believed the chances were extremely small that the baboon transplant would work. "This will probably hasten his death," said Dr Hugh Auchincloss Jr of Massachusetts General Hospital.
But the panel appeared to be moved to recommend that the experiment should go ahead by impassioned appeals from members of Mr Getty's family. "What if you are sitting on a solution to my brother's life and he dies?" his sister asked.
Mr Getty's mother said her son was aware of the risks involved but wanted the chance to help find a cure for Aids. "He doesn't want to die in a hospice. He wants to die fighting."
A final decision on the transplant is expected from the FDA within a month. But it is likely to heed the recommendation made by the 22-member advisory panel of doctors and scientists who heard testimony from the patient's family and Aids specialists at the University of California.
The panel asked researchers to try to find better baboons for Getty's donation because the two lined up were infected with five known viruses. However, it said that if better baboons could not be found and Getty wanted to take the chance the FDA should allow the procedure anyway.
Doctors from San Francisco General Hospital and the University of Pittsburgh say there is a small chance that baboons could hold the key to boosting Aids patients' immune systems because the animals do not get infected with HIV-1, the virus that causes most Aids cases in America.Reuse content