Until now it was not known whether eggs obtained in this way could survive thawing to be fertilised.
The advance spares women from taking risky fertility drugs that can cause a rare, yet deadly condition - ovarian hyperstimulation syndrome (OHSS).
Canadian researchers told a fertility conference in Lyon three others are expecting babies by the same process.
The findings hold particular hope for patients with cancer-related fertility problems.
Chemotherapy can cause infertility and, therefore, some women with cancer opt to have their eggs collected and frozen before they start their cancer treatment.
But not all women will want or be able to delay having chemotherapy to undergo ovarian stimulation.
Certain tumours, including some breast cancers, can grow if the woman takes drugs to stimulate the ovaries, for example.
Early stages
Dr Hannal Holzer and colleagues at the McGill Reproductive Center, Montreal, cautioned that their technique - in vitro maturation or IVM - had not yet been tried on women with cancer.
The women they studied had polycystic ovarian syndrome (PCOS) - a condition where the ovaries are covered in cysts which can impair fertility and which is linked with an increased risk of OHSS.
Of 20 women, four achieved pregnancy with the technique.
Dr Holzer said: "Until now, it was not known whether oocytes collected from unstimulated ovaries, matured in vitro and then vitrified, could survive thawing, be fertilised successfully and result in a viable pregnancy after embryo transfer.
"We have demonstrated for the first time that it is possible to do this and, so far, we have achieved four successful pregnancies, one of which has resulted in a live birth."
He warned the research was still in its early stages.
Moderate or severe ovarian hyperstimulation syndrome can occur in 3-8% of IVF cycles.
Expand choices
Professor Robin Lovell-Badge, of the Medical Research Council's National Institute For Medical Research, said: "Each step in this work had been achieved before, but this is the first time they have been successfully strung together.
"It is important as it will expand the choices available to women with diseases of the ovary or cancer and the clinicians treating them."
Dr Laurence Shaw, spokesman for the British Fertility Society, said: "These pregnancies are an exciting step. However, the pregnancy rate is very low and therefore large numbers of eggs would be needed."
He stressed that it was a treatment suitable for people with fertility problems linked to conditions such as PCOS or cancer, and not for women who merely want to delay having a family.