Here's the full number
If you go to YouTube, Mr. Preston is credited both on this video and the commercial video.
This is a quote from Wiki -which must mean it's true... :-) (but it is!)
"In 1961, Preston was asked to make a recording as part of a program by the President's Council on Physical Fitness to get schoolchildren to do more daily exercise. The song, "Chicken Fat", which was written and composed by Meredith Willson and performed by Preston with full orchestral accompaniment, was distributed to schools across the nation and played for students in calisthenics every morning. The song later became a surprise novelty hit and part of many baby-boomers' childhood memories."