It happened in Antarctica in 1961. The doctor — and patient — was one Leonid Rogozov.
“The operation started at about 22:00 on 30 April with the help of a
driver and meteorologist, who were providing instruments and holding a
mirror to observe areas not directly visible, while Rogozov was in a
semi-reclining position… Rogozov made a 10-12 cm incision and
proceeded to expose the appendix.”
More from the British Medical Journal.