Chimera - I Am My Own Twin
Identical twins: monozygotic (one zygote) -- twins form when a single fertilized egg splits into two genetically identical parts. The twins share the amnion and placenta and the same DNA set, thus they may share many similar attributes. (They don't share identical fingerprints.) They usually look alike, however, since physical appearance is influenced by environmental factors and not just genetics, identical twins can actually look very different, but they are always the same gender.
Fraternal twins: dizygotic (two zygotes) -- twins develop when two separate eggs are fertilized and implant in the uterus. The genetic connection is no more or less the same as siblings born at separate times. They may or may not look alike, and each twin can be of either gender.
Some scientists have theorized a third, hybrid type called polar body twinning, that occurs when an unfertilized egg splits into two parts and each part is fertilized by a different sperm. The twins would then share one-half of their gene set (from their mother). Because it is the father's DNA that determines the sex, each twin can be either gender.
A chimera is when two separate zygotes fuse into one, forming one embryo which contains the separate genetic material of each of the two zygotes. The chimera should have been a set of fraternal twins, but instead is one individual having two sets of genetic material. A blood test would reveal one genetic profile while a tissue sample from another part of the body would have the genetic makeup of a totally different person.
I immediately did some googling and discovered this fascinating article (published in the "New Scientist" magazine) on one particular case study -- "click" to read the complete article.

All this sounds like the stuff of science fiction, but then, so much science fiction turns out to be glimpses into the yet-unknown or that which has yet to occur.
With all the possible combinations and mutations that could happen, it's really phenomenal that so many of us humans are actually born normal ...by that I mean ten fingers, ten toes, one head, etc. Sure, there are many deformed babies, some are naturally formed so, while others are affected by external stimulus. My mother smoked and drank all during her pregnancy [with me] ...back when it was not suggested that you shouldn't. I was lucky to have not suffered any birth defects ...or was I? I secretly lay the blame for all my neurosis on [her] prenatal behavior. (Just joking, Mom.)

I too saw this program and was incredibly fascinated. CSI actually had an ep where a man had this very condition.
I saw that CSI episode also. The writers often base their scripts on actual human situations ...you couldn't make this stuff up.