At Popperfont, the great David Ng discusses the biological and/or evolutionary steps necessary to produce a theoretical real-life unicorn. I find it delightfully ironic that his first possible route involves something that, if I were to show you pictures of it*, you would probably request a unicorn chaser.
Basically, some kinds of tumors can produce little horn-like protrusions from the surface of the skin. (Sometimes these tumors are malignant, sometimes not.) If the tumor formed right in the middle of a horse's forehead ... et voila! You've got a unicorn.
This is not as unlikely as it sounds, by the way. The Mutter Museum has a wax model of the head of a French woman, Madame Dimanche, who had one of these tumor horns removed from the middle of her forehead when she was 82 years old. This happened sometime around the beginning of the 19th century. At the time of removal, the horn was 9.8 inches long.
And, yes, this would be roughly the same way that you get a jackalope.
*Needless to say, all links shall be followed at the viewer's own risk. I am not responsible for lost appetites.