A 31 year old woman in Manhasset, New York. apparently gave birth to identical triplets. This is despite the fact that only a single embryo was transferred (or so we are told). The press release from the the AP quoted a doctor who is a “specialist in multiple births” as stating that this was “an event so rare that it might happen just once in 200 million births.”

Well, not quite. If the pregnancy was conceived without the use of IVF then that might be a possibly correct estimate. However, if the embryo transferred was a blastocyst, that is an embryo that was cultured for five days in the laboratory, then the chance for the embryo splitting is much higher than the standard rate.
Most multiple pregnancies in in-vitro fertilization occur as a result of transferring multiple embryos to the uterus. However, it has been well described in the medical literature that the chance for identical twinnng is increased with IVF and with blastocysts the chances are even higher.
In fact, the rate of identical twinning in blastocyst transfers is about 1%. so while the chance for a split causing an identical triplet is still low, it is a much more common event than described in the press release and hardly warrants a breaking news story.