From the series "Weird Or What" first broadcast 6-9-10.

Two
separate fertilized eggs can fuse together in utero, eventually forming
what is essentially one person with two completely different sets of
DNA. Lydia Fairchild is one such "Chimera". Her blood, saliva and
certain other parts of her body have one set of genes, while her
ovaries, uterus, and other parts have another. This means any children
she might have will share their father's DNA, but only one set of hers.

From Wikipedia:
"Tetragametic
chimerism is a form of congenital chimerism. This condition occurs
through the fertilization of two separate ova by two sperm, followed by
the fusion of the two at the blastocyst or zygote stages. This results
in the development of an organism with intermingled cell lines. Put
another way, the chimera is formed from the merging of two nonidentical
twins in a very early (zygote or blastocyst) phase. As such, they can be
male, female, or hermaphroditic.

As the organism develops, it
can come to possess organs that have different sets of chromosomes. For
example, the chimera may have a liver composed of cells with one set of
chromosomes and have a kidney composed of cells with a second set of
chromosomes. This has occurred in humans, and at one time was thought to
be extremely rare, though more recent evidence suggests that it is not
as rare as previously believed."

*Totally ripped from http://www.youtube.com/watch?v=oE908SNlKAY* - jackal452