The density of the atmosphere is so low at such heights that a parachute wouldn't function. Think about how a parachute actually works; basically the fabric smacks into air molecules and slows down. If there are very few air molecules to smack into it wont slow very much. The result is that the astronaut is going very, very fast already by the time the parachute starts working, and they're going so fast that they start burning up.
The Red Bull Stratos is probably about as high as you could possibly fall from and still have a parachute work.
