How to de-mob a deep/large underground chasm in Minecraft?

Solution 1:

For spawning purposes, the absolute best thing to do would be to fill the ravine with solid blocks. If I recall correctly, this makes the spawning algorithm give up on the space sooner so that you'll get slightly higher spawn rates elsewhere. However, that's probably not practical.

I would recommend simply lighting it up with torches, starting from the top down. Yes, there will be ledges on the side; such ledges are generally flat and lengthy, so you can deepen them by digging into the wall a little bit to have a continuous normal walking path, and light that up. As you light up the ledge you will start to get a better view of ledges on the other side. As a bonus you might find passages to other caves you'll want to light up.

The reason to go top down is so that you don't have monsters falling on your head. The particularly problematic ones are creepers, which in recent versions may instantly explode if they drop from a height next to you. If this particular ravine does not have many ledges, or there are many spawning spaces outside of the ravine, it may be safe enough to light up the floor first; this will get rid of most of the spawn area and so you'll get fewer skeletons shooting you while you deal with the ledges.

I would not recommend using lava or water as fill, because they will make things inconvenient if you later decide to build some underground structure that just happens to intersect the ravine's location.

No monsters, not even spiders, spawn on walls, so you don't have to light up sheer walls (or any part that is not a floor or a ledge).

Solution 2:

Lava seems like the best option to me. You can just place a lot of it on the walls of the ravine, about five blocks apart. That should stop most of the mobs from spawning.