Sometime between Gen. 1:1 and Gen. 1:2, all the unicorns vanished from the face of the planet. No one is sure just why, but the current thinking is that they got left off the ark.
There were green alligators and long-necked geese
Some humpty-back camels and some chimpanzees
Some cats and rats and elephants, but sure as you're born
The loveliest of all was the unicorn