Bride Paola Podest and groom Carlos Ciuffardi said "I do" after telling Francis that they had been married in a civil service in 2010.
However, they said they were unable to follow up with a church ceremony because of the 2010 earthquake that hit Chile.
Francis then offered to marry the LATAM flight attendants aboard the aircraft en route to the northern city of Iquique, and they both readily agreed.
The head of the airline served as the witness.
Mr Ciuffardi told journalists in the aisle of the Airbus 321 that Francis told him it was "historic", and no pope had ever before married a couple aboard a plane.
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