In the world of hybrid animals, we have horses and donkeys getting together to create mules, and lions and tigers getting together to create ligers.  Both of these hybrids are fairly common, because their source species (like horses and donkeys) are not very far apart, evolutionarily speaking.

However, goats and sheep are quite unrelated.  They may look similar to the untrained eye, and serve similar purposes in the barnyard ecosystem, but sheep have only 54 chromosomal pairs, while goats have 60.  Goats and sheep belong to different genera, goats being from the genus Capra and sheep being from the genus Ovis.  

Just to put this in perspective, cats and dogs are also from different genera, cats from genus Felis and dogs from genus Canis.  I'm not aware of any cat-dog hybrids, despite their long history of being housed together as well!  It seems that sheep and goats are just barely related enough to occasionally breed.

These couplings almost never produce an offspring, and those that do almost never produce a live offspring.  When they do, it is usually called a "geep."  A recent geep named Lisa was born in northern Germany, to a male goat and a female sheep.  Lisa has the coloring and agility of a goat, but the small stature and hanging tail of a sheep.

Another geep, dubbed "The Toast of Botswana," was born in Botswana in 1994, to a female goat and a male sheep.  Samples from the hybrid were sent for testing, and it was found to have 57 pairs of chromosomes - halfway between the number its mother and its father have.  This hybrid looks more like a goat with a white sheep-like coat and a sheep's hanging tail.

Natural hybrids often have in-between features, like the Botswana geep's coat which has a sheep's wool for its inner layer, and a goat's coarse hairs for its outer coat.  However, mosaic hybrids will have patches of pure examples of one parent or another.

Mosaic hybrid geeps have been created in the lab, by fusing the embryos of sheep and goats together.  This creates an animal known as a chimera, which has two very distinct groups of cell populations.  

Imagine two cooking experiments: in one, you whip a raw egg with a cup of milk and cook it.  This creates an omelet, which has the mixed components of both "parents," like a natural hybrid.  In the second experiment you mix a chopped-up hard-boiled egg with cubes of cheese.  This will be a bowl of distinct pieces of either egg or cheese, like a chimera.  The un-mixed nature of the chimera is called "mosaicism."

Chimerism can very VERY rarely happen in the womb, but is rather more common in labs.  Scientists who created a chimera geep found that its coat was patchy, with distinct patches of sheep's wool and goat's hair.

Chimeras have also turned up on TV dramas, including a killer on "CSI" who had two different DNA profiles thanks to his mosaicism.  Genetic mosaicism has also been mentioned a few times on the medical drama "House," which specializes in bizarre and ridiculously rare medical conditions.