Well, it only took me 51 years, but I've finally heard the original version of "The Twist". By Hank Ballard. This morning on Sirius/XM 50s on 5.
I think this is the correct version: http://www.youtube.com/watch?v=hPjxoy7lsE8 Sorry for the ad, but it is the only version that I could find.
Since I started listening to Top 40 Radio (CFUN, in my case) in early 1962, Chubby Checker's version had already hit #1 twice, so nobody was playing Hank's version as an Oldie.
For those unfamiliar with the story, Hank wrote the song, and it was the B-side of a minor Top 40 hit in early 1959. In 1960, Dick Clark, while doing American Bandstand, asked a Detroit teen what the hot new dance was in Detroit, and the teen replied "The Twist". "You mean that old Hank Ballard song". "That's the one".
Dick was not willing to have Hank on his show, because so many of his songs were considered "dirty", so Dick's wife Bobbi suggested a local Philly singer Chubby Checker because he was so good at impressions of other singers. Chubby had had one small hit previously, "The Class", where he does some of those impressions: http://www.youtube.com/watch?v=vJN8KTeOh34
Dick got Chubby to do a pretty close clone of Hank's original version, and the rest is history.