I haven't been able to verify this at all, but if it's true it might be the Best Science Fair Project Ever. Ten-year-old (at the time) William T. Wood, fresh from his 2002 science fair win for a project on silica aerogels, he decided to kick it up a notch and see if silica aerogels could be made at home. And by "made at home", I mean "without the really expensive equipment previously thought to be essential."
The article goes into great detail, enough for a handy GeekDad to use as a how-to. The process is based on one listed at the Lawrence Berkeley Laboratories, with enough notes and modifications and tips to give the strong impression that this really did happen, and successfully. So, who's going to be the first to try this out?
(Note: if you aren't sure why silica aerogels are completely awesome, be sure to read the Times Online overview article about aerogel applications.)