David Letterman -- Running Around Like A Chicken ... With Its Shoes Cut Off

Oh boy ... David Letterman snuck out of his island retirement home without his shoes again ... at least it looks that way.

Dave was down in St. Barts this past weekend mentally preparing to step down from the 'Late Show' when he took an early morning Caribbean jog ... sans shoes, only socks.

There's a ton of studies about the benefits of jogging barefoot ... and Dave's embracing all of them during his island time.