Physicist: Yes and no, but mostly no.
It’s certainly possible to parachute safely to Earth from the top (or nearly the top) of the atmosphere, but this question isn’t about parachuting from space it’s about parachuting from orbit. An orbit isn’t just a matter of being very high, it’s mostly a matter of being very, very fast.
When you throw something it follows a curved path that eventually intersects the surface of the Earth (technically this is already an orbit, it just gets interrupted by stuff in the way). If you use a cannon, then the curve straightens out a bit but it still intersects the surface of the Earth, just farther away. With a really, really powerful cannon (or more likely: a rocket) you can get something moving so fast that the curve of its fall matches the curve of the Earth. When this happens the object is in orbit; a closed loop around the Earth that repeats forever.
You may have noticed that the Earth isn’t terribly curved, so it may seem that you’d need to be moving impossibly fast to follow it. That’s exactly the case: above the air but near the surface of the Earth you’d need to be moving sideways at about 8km/s. This is more than 23 times faster than the speed of sound. Not slow.
This 8 km/s speed corresponds to the lowest, slowest (when you hit the atmosphere) orbit. Any other orbit either won’t bring you close to the atmosphere or will do so faster (at up to about 11 km/s). Being the slowest and lowest, these roughly circular “near Earth orbits” are very popular (that is to say: cheap). Near Earth orbit is probably what you’re imagining when you think of parachuting to the Earth.
So here comes the point. You can go as fast as you want if you’re doing it in space, but when you’re measuring your speed in km per second, air starts to feel like concrete (hot concrete).
When an object plows through air at very high speeds it tends to burn, shatter, and shred. Parachutes are used for most entries and reentries, but not initially; most of the deceleration from orbit is handled by heat shields, which are a cross between parachutes and bricks (or a brick and another kind of brick). Once enough of a falling object’s speed has been shed by a heat shield (typically slower than sound, but up to a few times faster), it is then safe to deploy an actual parachute.
If you were to jump (fast) out of the International Space Station with the aim of entering the atmosphere and deploying your chute, you’d find it filled in short order then torn to ribbons shortly after. Like any falling star, you’d find yourself hot, dead, and profoundly luminous. Like icy meteors, you’d probably flash into steam and air burst before reaching the ground.
The reason you can’t parachute from orbit is simply a matter of engineering. We haven’t yet created parachutes that can survive being deployed, and then work properly, at speeds above around mach 2. At reentry speeds, which are in excess of mach 23, parachutes just can’t hold up. However, someday it may be possible. We know that the accelerations involved are survivable, and there don’t seem to be any fundamental limitations, we just need better materials and techniques. Also, for at least a little while, a spacesuit capable of reentry on its own (before the parachute has had a change to slow it) would be nice.
Merely falling from space is probably pretty easy. The highest jump so far was from 24 miles up. A jump from space is a mere four times higher. You’d need a rocket instead of a balloon, but aside from being a silly thing to do, there’s nothing stopping someone from doing it.