Among the Greeks, the unicorn was considered a real beast, and Ctesias in his lost History of India (in fragments as preserved in Photius, Biblioteca, codicil 72) describes one as a wild ass of many colors, complete with a horn a cubit long: "In India there are wild asses as large as horses, or even larger. Their body is white, their head dark red, their eyes bluish, and they have a horn in their forehead about a cubit in length." It lived in India, and Ctesias' description appears to be a conflation of several different animals, including perhaps the rhinoceros.
Unicorns also occur in the Bible, or, more accurately, translations of the Bible. The original Hebrew word re’em, referring to an untamable horned beast of great strength, was translated into Greek as monoceros (one horn) and Latin as unicornis (one horn), yielding the King James “unicorn” of Job 39:9–12; Ps. 22:21, 29:6; Num. 23:22, 24:8; and Deut. 23:17. (Thanks to the Jewish Encylopedia for the list!) Oddly enough, Jewish lore apparently also held that the unicorn had fur of many colors.
What I find interesting is the suggestion that this translation occurred due to an artistic convention from Mesopotamia misunderstood by later peoples. The re’em is apparently cognate with the Assyrian rimu, a great and powerful bull with mighty horns, probably an extinct auroch. The auroch changed colors during life, being born reddish-brown, turning black in adulthood (bulls only), and retaining a large white stripe, a lighter colored “saddle” marking, and tawny fur around the mouth. This probably gave rise to the multi-colored claims for the unicorn, typically expressed today with an association between unicorns and rainbows.
The Assyrians frequently depicted the rimu in profile, so that its two horns were placed one before the other, meaning that the Assyrian images of the horns appeared as a single horn emerging from the bull’s forehead. When the Bible was translated into Greek, somehow this artistic convention got carried over, making verbally explicit the depiction of the auroch in art.