That is one of the few things I REALLY want to do....
Absolutely.
(5 miles of brown paper, 100 gallons of paper glue, 10 miles of string...... etc.)

I may be wrong, but I think that something known as "terminal velocity" will prevent him from getting anywhere near the sound barrier.

Sign me up. Please. Pretty please. With cherries.

In normal atmospheric pressure the max speed a skydiver can reach is only about 130mph. But way up at that altitude where the air is thinner he could reach much more than that. Also when his body does break the sound barrier it will be less stress on him, again due to air density.

Speed of sound in space = 0 m/s Speed of Sound at 102000 ft (31090m) = 327 m/s Speed of Sound at sea level = 343 m/s (Woolfram alpha)
Um 100k ft is not even half way to space...
Still plenty of air resistance....
Maybe he can get to 300 miles per hour (133 m/s)
Still a long way to Speed of sound....
Like to hear the boom...
Also, Probably the sonic buffet would vibrate a human body to pieces, and if not, merely kill the person...
We all need adventurers to do the things we can't afford to do.

@MD The article states that Kittinger reached 614mph in his jump from 102,800ft

According to this article, he achieved 690mph shortly after jumping. http://www.nytimes.com/2010/03/16/science/16tier.html?_r=1&src=me&ref=general There was a program on television (don't remember which) that estimated he topped out at around 800mph.

Why, with 26 pictures attached to this article, is there not a single one of him actually jumping from 71K feet?

What a supreme waste of resources!

It isn't a waste of resources at all if you stop looking at this through the eyes of a commoner. Sure it's an absolute thrill if you were the one to jump and set a new record. But the important thing is to learn the effects and the extent of it to a human being who free falls at such height, with a pressurized suit of course. That knowledge will come to use when astronauts need to make an emergency jump at such heights mid flight or return.