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Duane Eddy's "Some Kinda Earthquake" in 1959, 1 minute and 17 seconds.

some links found on the way to this info

discussion of short songs
http://www.stevehoffman.tv/forums/archive/index.php/t-47442.html

music trivia
http://www.bodees.com/Bodees/oldtrivia.htm

List of Billboard Hot 100 chart achievements and milestones

http://en.wikipedia.org/wiki/List_of_Billboard_Hot_100_chart_achievements_and_milestones

Record Breakers and Trivia UK Record Breakers and Trivia

http://www.everyhit.com/record.html
I thought I'd always remember who wrote "Thirty-six Second Song" (NOT the one you find in the Google search), only I don't. I do remember the complete lyrics and melody, complete with steel guitar outro:

All the DJs say
That songs today run much too long
And so that's why I went and wrote
This thirty-six second song
Guess it beats The Minute Waltz.... by 24 seconds....

I'm pretty sure it didn't make the us or uk top 100 chart, this one gets us off the stage quickly when nature calls.

https://www.youtube.com/watch?v=X30l7A8-BRM
Ok, so I misread the topic and thought you meant what was the shortest song title and my guess for that would be S.O.S. by Abba.

As for shortest song to get on the charts - I'll admit I was too clueless to guess.
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