Yea, we did that back in the 1950s, but that was with the benefit of an airframe around the human. Felix Baumgartner is going to do it (Steve Kotler, PopSci) without such trivialities:

The Suit That Will Help Felix Baumgartner Withstand A 120,000-Foot Free Fall

Pure oxygen?

I don't know about that.

One short in the heating system and he's going to be a falling star.

I think it's much more likely the the G-forces of an uncontrolled spin or the wave when breaking the sound barrier will be far more dangerous.

That perked my curiosity, too. But then I figured he'll be wearing a respirator and not freely breathing with the helmet filled with pure oxygen.