The best way to make a chasm on land is the way nature does it- slowly, and with water. As AndreiROM points out, the rapid appearance of a chasm is going to displace a huge amount of rock, proportional to the size, and that's going to have even larger effects on the planet, and even magic won't change that. Additionally, as David Lago points out, there are fundamental limits on the height of structures in a gravitational environment. Check out this site for the math about how tall a mountain could be, and essentially reverse the logic to get maximum depth on Earth- about 10km. If you decrease the size of your planet, you can go even deeper and get something more like the Valles Marineris on Mars, which isn't as narrow but is definitely huge.
However, even canyons that have been carved by water are extraordinary- I'll let the picture speak for itself.
The Grand Canyon is still tectonically active, but I believe it's stopped getting deeper because it's getting filled in more rapidly than it erodes, mostly due to humans removing the erosive water for use elsewhere. If this is chasm-like enough, you could argue that your planet simply allows for it to grow deeper. First, change the geology to be mostly limestone or sandstone, both of which have a high angle of repose, allowing them to form even steeper sides. Second, have the river drain from high mountain areas with consistent snowfall to ensure semi-constant erosion. With those qualifications, you could probably justify a chasm ~8km deep.
If you're especially eager to have it happen overnight, you'd have to handwave a little bit. Maybe there's a massive internal lake blocked off by some kind of dam that collapses, allowing the water to flow out very rapidly. These are called outburst floods and they were relatively common during ice ages. This still wouldn't happen overnight and wouldn't produce something as steep as the Grand Canyon, but it'd be faster if that's what your plot requires.
The other thing I want to mention here are the chasms in the ocean. The smaller of the two are the submarine canyons, which could be exposed by a reduction in sea level as water is stored as ice in the poles during an ice age. Congo Canyon starts at a depth of just 26 meters, and could be further exposed from there.
If you evaporate all the water off your planet, like what scientists currently believe happened on Mars, you'd be left with the subduction trenches. These are seen in the Heezen-Tharp map below at the northwest portion of the Pacific, along the Ring of Fire.
I believe these are the largest chasm-like structures in the solar system, so they might be what you're looking for.