Parents Naomi Findlay, 31, and Dean Wilkins, 43, had discovered when Ms Findlay was nine weeks pregnant that their baby had ectopia cordis but hoped that she could be treated at birth.
Her parents, Naomi Findlay and Dean Wilkins, of Bulwell, Nottinghamshire, said the first scans led doctors to tell them that "termination" was the only option.
Glenfield Hospital says it doesn't know of any other babies in the United Kingdom who have survived the condition. "I had brought an outfit to (the) hospital that she could wear if she died", Findlay said in a statement. "When we did the research, we just couldn't physically look because the condition came with so many problems".
"We were told that our best bet was to terminate", Wilkins said. They went through counseling to understand the risks and chose to go forward with the pregnancy.
Baby Vanellope is doing well, but her prognosis is uncertain. "But when she came out and she came out crying, that was it". When she cried, we cried.
"We know this is going to be a rollercoaster and have started to prepare ourselves for the hard times ahead, but we needed to give her a chance", Wilkins said in a statement.
Three-week-old Vanellope Hope Wilkins was delivered by a team of 50 medical professionals at Glenfield Hospital in Leicester, UK, on November 22.
"At around 50 minutes of age, it was felt that Vanellope was stable enough to be transferred back to the main theater where she had been born to the waiting anesthetists, congenital heart disease and pediatric surgical teams who began the task of putting her entire heart back inside her chest", he said".
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Newborns normally have an indent on their left lung which creates space for the heart to fit in but Vanellope did not have this.
She is now three weeks old.
This allowed staff to carry out the final operation which involved taking skin from under her arms and moving it round to join in the middle of her body. As her organs fight for space inside her chest, she is still attached to a ventilation machine.
Babies born with ectopia cordis usually have a 1 in 10 chance of survival.
East Midlands Congenital Heart Centre lead surgeon Branko Mimic said: "Cases such as Vanellope's, where everything else appears essentially normal, are even rarer, and whilst therefore it would seem more hopeful she will do well, it is therefore nearly impossible to be confident of this".
Glenfield hospital paediatric cardiologist Frances Bu'Lock says: "There may be strategies whereby we can put some internal bony protection in whether that's with 3D printing, either of something plastic or maybe even something organic that might grow with her".
She said: "I had seen one in foetal life around 20 years ago but that pregnancy was ended".
Special lines were made to insert into her umbilical cord to give fluid and medication to support her heart. "I felt hopeless and just held onto Naomi and was staring into her eyes praying that it was all going to be ok".