A organ transplant
involving the donation of one organ from one species to another. This has happened many times, such as a baboon heart transplant
to a human, or the usage of pig heart valves
The problem is, aside from the heart valves themselves, the transplants don't work very well. Xenotransplants cause Hyper-acute rejections of the tissue, meaning the transplant usually won't take root, as the body's immune system attacks it. There are some medications that can suppress the immune system's response, but there's still masive inflamation and the situation gets hairy for a while as the prognosis is up in the air.
Originally there was a large debate against this form of transplant, a disease in animals could possibly cross over into humans, becoming a new epidemic. The CDC is looking into it.