Reached by a long drive into Lincoln National Forest, Last Chance Canyon has a remote feel to it.
Tall, beautiful limestone cliffs make up the canyon walls, and although the canyon is a fine hiking destination just for its scenery and feeling of being far away from everything, the canyon primarily attracts climbers because of the very good single-pitch sport climbing there. (Although a few trad lines exist, almost everything is sport.)
The limestone routes are not (yet) polished, and they range from 5.4 to 5.13+.
Over a dozen developed crags exist, and because I have only been there once, I am not going to list or describe them all because, frankly, I do not know enough about them to do so. I will be attaching one crag page, but for more information, please go to the Mountain Project page.
The MP page has these directions: "From US 285, ~8 miles N of Carlsbad, head West on Highway 137 to Queen(~38 miles). On the far end of Queen, just after Mile Marker 18, turn right onto Forest Road 525 (signed). There are numerous spur roads, just follow the main track. You will encounter 2 cattle guards and two gates. After ~3 miles, make a hard left onto 525A (signed), and continue 1 more mile to the parking lot overlooking the canyon, passing an old shack."
There is at least one other way, and it makes more sense if you are leaving from Carlsbad or approaching from Whites City (the little town outside Carlsbad Caverns NP).
Somewhere around halfway between Whites City and Carlsbad, look for a road signed for National Forest Access, including for Sitting Bull Falls. Follow this road into the desert. When it intersects another paved road, turn left. You are now on the way to Queen and should use the directions above.
High clearance is recommended.
I can't remember the mileage, but the drive in from Carlsbad Caverns took about 90 minutes.
From the parking area, find the trail marker and hike down into the canyon. Once you reach the bottom, where you go depends on which crag you want to find.
There is a bolting ban in effect; you may not bolt new routes without permission from whoever oversees the area.
There is free camping by the trailhead. You can also camp down in the canyon.