I remember reading some years back how missionaries in Tibet were told stories of how prevalent in the 1800's the belief that there were unicorns living in the mountains of Tibet!
Do any ancient Tibetan unicorn myths exist?
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Well, here's one.
The existence of these Eurasian nomads called the Qiang, who were known as the “goat people” and who practised animals ordeals, may help to account for the fact that later in the West there was “a vigorous and widespread belief in a unicorn inhabiting the table-lands of Tibet—a region included with the “India” of Ctesias—(which) can be traced in existing documents as far back as the time of Genghis Khan, and there is good reason for supposing that it is much older still” (Shepard  1982, 32). The reality which lay behind this notion was the presence in Tibet of an elusive long horned wild “antelope” called the chiru by the Tibetan nomads, or, by the Mongolians, the orongo (colour plate 7).
So basically, they thought an antelope was a unicorn. As far as I know, it never did anything. I think it's name was "Serou".
You might find this interesting:
It describes a prehistoric rhino-like animal, Elasmotherium sibiricum or the ‘Siberian unicorn’ with a single long "horn" on it's nose which may have lived alongside humans.