The oldest living Olympic athlete is Yvonne Chabot-Curtet, who represented France in the long jump in the 1948 London and 1952 Helsinki games. She is 104 years old.
The oldest living American Olympic athlete is Iris Cummings, who represented the US in swimming in the 1936 Berlin Olympics. Yes, those Olympics, with Jesse Owens and Adolf Hitler and filmed by Leni Riefestahl. She is 103 years old. She also holds the record for the earliest competition of any living Olympic athlete.
Here are all of them.
The list of Olympic cetenarians is here. A while ago, Wikipedia decided that simply being in the Olympics didn't merit an entry, so many of these people are only listed under their team pages, if at all.
