In a video that media said had been uploaded to her Facebook page on Sunday, Valentina Maureira said from her hospital bed: "I am asking to speak urgently to the president because I am tired of living with this sickness and she can authorize the injection to put me to sleep forever."
Cystic fibrosis is a genetic condition that affects the lungs and other organs.
Maureira's brother had died of the disease, her father, Freddy Maureira, told local Radio Bio Bio.
"She has already had five operations... which have caused her a lot of suffering and pain," he said. "It was promised that things would get better, but for her it was worse."
The video had surprised him, he added.
A spokeswoman from the Universidad Catolica clinic in Santiago confirmed that Valentina Maureira was a patient at the hospital and said she was stable, with no immediately life-threatening conditions.
In Chile, as in many countries, euthanasia is against the law. The Catholic church retains a strong influence on society, and the country is one of a handful to ban abortion under any circumstances.
Center-left Bachelet, who is a year into her second term, has introduced reforms, including a bill being debated in Congress that would relax the abortion law, that have angered conservatives.
Bachelet's agenda has not mentioned euthanasia, though, and the government has not yet commented on the Maureira case.
