Diana Nyad set off from Havana late on Sunday. She is hoping to arrive in Key West in Florida on Wednesday.
The US and Cuba - two former Cold War adversaries - still have no formal diplomatic relations.
It took more than a year of negotiations to get both countries to allow the epic swim to take place.
Ms Nyad was one of the world's greatest long-distance swimmers back in the 1970s, but she failed in her original attempt to complete the crossing from Cuba in 1978, when she was 28.
Now at the age of 61, she has decided to re-enter these shark-infested waters and try once again the gruelling 103-miles (166km) swim between Havana and Key West.
Before setting out, Ms Nyad told reporters that although she retired from competitive sport 30 years ago, she was fulfilling a lifelong dream.
"All my life I dreamed of being the first one ever to swim across without a shark cage," she said.
"I never thought I'd come back to this sport. It's a gruelling sport - it's for the young."
There will be no sleep for Ms Nyad for the next three days - just brief pauses in the water every 90 minutes to take in food through a plastic tube.
It is a massive undertaking, with support boats carrying everyone from medical assistants to nutritionists along with a shark protection team.
These include two kayaks paddling beside her the whole way equipped with underwater electrical shark shields and just in case those do not work, there is also a team of divers who can jump in and keep them at bay.
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What world leader do you admire?The President of the United States because he gets to make important decisions and run our Country. How would you change the world?Tougher laws on