Hobbits are not sapiens.
In 2003, a team of anthropologists discovered the skeletons of what appeared to be miniature humans living some tens of thousands of years ago on the island of Flores. The big question was, were these simply small and possibly deformed Homo sapiens, or something else entirely?
If the beings were modern humans, the specimens discovered may have been individuals suffering from some form of microcephaly. This is a condition which leads to much smaller than normal brain and skull size.
On the other hand, if these specimens represented an entirely different species, this would mean that there were other hominids on earth for much longer than previously suspected. The population on Flores Island is believed to have lived there from about 95,000 to about 18,000 years ago. To put that in perspective, Neanderthals disappeared about 30,000 years ago. Modern humans evolved in Africa around 200,000 years ago.
Recently, William Jungers and Karen Baab of Stony Brook Medical Center have put this controversy to rest. They performed a detailed analysis of the fossil remains, comparing them to modern humans, including those with microcephaly, and to chimpanzees. Their conclusion? Homo floresiensis is a separate hominid species and not a form of Homo sapiens at all.
So where did this species come from? There were several waves of hominid emigration from Africa, one by Homo erectus over a million years ago, reaching south Asia well before the appearance of Homo floresienis. Although Homo erectus is now extinct, their descendents could have included the Floresians. If so, they would have undergone extreme dwarfism, not unknown among animals adapted to island life. A good example of this is the Channel Islands mammoth, which was less than half the size of its wooly cousin.
Later, true humans migrated out of Africa, and their descendents are all of us. They may have reached Flores island before Homo floresiensis became extinct, leading to some interesting interactions.
UPDATE: A new paper by Charles Oxnard of the University of Western Australia has reopened this controversy. According to his findings, Hobbits were not a separate species after all, but instead were modern humans suffering from hypothyroid cretinism due to low iodine.