The moon is small, meaning its gravitational forces are less likely to collapse large massive cliffs like this. The freefall time from that height is 4.2 minutes. Miranda, a moon of Uranus, has cliffs at least 10 km high. You could launch yourself off it and fall for 8.4 minutes. Of course, you'd need some way to stop from slamming into the cliff's base -- at the bottom of Charon's cliff you'd be traveling at 160 miles per hour, and 89 mph at Miranda's -- and of course parachutes don't work in a vacuum.
Anyway, this is all just an excuse to post this wonderful video by Erik Wernquist called “Wanderers.”
It shows people (I assume they're humans) jumping off the cliff of Miranda, and an inspiring view of a space elevator. (Space elevators are more feasible on smaller bodies; you could build a space elevator on our Moon out of a produced material called M5 (and almost Kevlar, but it has a tensile_strength/density ratio that's about 10% too low). There is no known material suitable for Earth; maybe carbon nanotubes, but just recently it was shown that that's not looking feasible. Someone will come with something, though, someday.)