Doctors in a hospital in Chicago have implanted two embryos which have been screened to make sure they match Michelle and Jayson Whitaker's son Charlie.
The family had been banned from having the procedure at a UK clinic.
Charlie suffers from a type of rare anaemia which increases his chance of cancer - or perhaps other fatal complications.
He could be cured by a transplant of special cells from the new baby's umbilical cord - as long as the baby's tissue was a near-perfect match.
Few matches
However, under normal conditions, only a small proportion of embryos conceived naturally or created through conventional IVF would be a match.
This would mean that the couple might have to have several further children before one matching Charlie was created.
After fertility treatment, nine embryos were produced, and doctors took a single cell from each at an early stage in development.
Best embryos
Each was tested and only those embryos which matched were considered for implantation.
Three fitted the bill, and the best two were implanted into 30-year-old Michelle.
The couple, from Bicester in Oxfordshire, now face an agonising two-week wait to see whether a pregnancy results.
There is less than a 50/50 chance of it working first time around, even though Michelle is relatively young.
If not, they will have to undergo further IVF treatment.
Charlie's disease affects only 50 children in the UK, and he currently needs blood transfusions every three weeks and painful injections almost daily just to keep him alive.
Even if the new baby is a match, there is only a tiny chance that it will develop Charlie's illness.
Stem cells
The umbilical cord contains a type of primitive cell called a stem cell which could help "kick start" Charlie's body into producing the red blood cells he needs.
The cells would be infused into him in a similar fashion to a bone marrow transplant.
The Human Fertilisation and Embryology Authority (HFEA), which regulates fertility treatment in the UK, ruled that while it was acceptable to test and select embryos to prevent the birth of a baby with a genetic disease, it was not ethically acceptable to select them in order to help another child.
Julie du Plessis, Education Officer for the campaigning group LIFE, said, "This case has pushed the boundaries of science too far.
"Children should not be created in order to serve the medical needs of older siblings.
"We are creating an industry where children are made to order, bought and sold."