Here ya go, Mark. I have heard it many, many times on the radio years ago:

THE UNICORN
(Shel Silverstein)
As recorded by Shel Silverstein on “Inside Folk Songs” (1962).

Well, a long time ago, when the Earth was green,
An' there was more kind of animals than you've ever seen,
An' they'd run around free while the world was bein' born,
An' the loveliest of all was the unicorn.

There was green alligators an' long-necked geese.
There was hump-backed camels an' there was chimpanzees.
There was cats an' rats an' elephants, but sure as you're born,
The loveliest of all was the unicorn.

Well, now, God seen some sinnin' an' it caused him pain.
He says, "Stand back, I'm 'onna make it rain."
Says, "Hey, brother Noah, I'll tell you what to do:
Go an' build me a floatin' zoo,

“An' you take two alligators, a couple o' geese;
You take two humpty-backed camels an' some chimpanzees.
You take two cats an' rats an' elephants, but sure as you're born,
Noah, don't you forget my unicorn.”

Well then, Noah was there an' answered the call,
An' then he finished up the ark just as the rain started fallin'.
He marched in the animals two by two,
An' called out as they went through:

“Hey, Lord, I got you two alligators, a couple o' geese;
I got you hump-backed camels an' some chimpanzees.
I got you cats an' rats an' elephants, but Lord, I'm so forlorn
'Cause I just don't see no unicorn."

Well, Noah looked out through the drivin' rain.
The unicorns was hidin', playin' silly games.
They were kickin' an' splashin' while the rain was pourin'.
Oh, them silly unicorn!

Yeah, two alligators, a couple o' geese,
Two hump-backed camels an' two chimpanzees.
Noah cried, "Close the door 'cause the rain is pourin'
An' we just can't wait for no unicorn."

An' the ark started movin' an' it drifted with the tide,
An' the unicorns looked up from the rock an' cried,
An' the water come up an' sort o' floated them away.
That's why you've never seen a unicorn to this day.

You'll see lots of alligators an' a whole mess o' geese,
An' you'll see plenty hump-backed camels, lots o' chimpanzees.
You'll see cats an' rats an' elephants, but sure as you're born,
You're never gonna see no unicorn.