Whoa, this show starts in 20 minutes. But it broadcasts many more times over the next month. There is an extremely unusual condition--it's thought to be rare, but then again, it's often discovered only be sheer accident, so who knows?--where two separate embryos fuse into one. The result: a Chimera, a person born with two separate sets of DNA.
Most of the time, there's no way of knowing or identifying the condition unless there are health or reproductive problems that call for DNA testing (like transplants, transfusions, etc.). But sometimes, the condition manifests itself physically: actual hermaphrodism, different-colored eyes--watch the Discovery Health Channel documentary, I Am My Own Twin to find out.
Some studies show that, like multiple births, chimerism may be more likely to occur with IVF, when several fertilized eggs are implanted at once.
Anyway, here's the text from a 2003 New Scientist article, "The Stranger Within"; here's a Telegraph (UK) synopsis mentioning a possible link to IVF and fertility drug treatments; and here's the DHC program page with a broadcast schedule.