Allmusic.com says CHOW WILLY was written by Josef Marais and recorded by Frankie Laine and Jo Stafford (as a duet).

Here's what I transcribed from a sample:

Borrow me a horse and away I ride
Chow Willy, chow Willy
Borrow me a whip and a saddle of hide
Chow Willy wee
Borrow me a whip and a saddle of hide
And I'm gonna make a red-head gal my bride
Rick tum a riddle umma rick tum a ree
Chow Willy wee

Someone else has been here since you've gone
Chow Willy, chow Willy
Stranger in the town and his name is john
Chow Willy wee
Stranger....