Options for woodchuck control include: cage traps, foothold traps, body gripping traps, snares, shooting, and gas cartridges. Each one of these devices has pro's and con's based on the situation. Personally, if you're only getting $5 per chuck, I'd recommend shooting with a .17 HMR.
However, if you need to trap them snares or body gripping traps would be the way to go. With snares, I like 1/16th cable about 20" long with a cam lock. For body gripping traps, I really, really, really like the 155. Both devices go into the den entrance. For snares, do a 4 or 5 inch loop 1/2" off the ground and make sure you stake them good. If you need forcing, do it with rocks or dirt that have already been excavated by the chucks themselves. Don't be surprised to find the snares knocked down about 1/2 the time and be equipped to deal with a live chuck when it connects. If you're using 3/32 coon or beaver snares, make sure to bring a shovel to help retrieve the caught animal (it's why I like short snares for them).
For the 155's, place them with the back jaw about 1/2" away from the opening right directly in the entrance with the trigger facing away from the hole. Stake them through the springs with T stakes to provide support and prevent loss. I've only had 1 or 2 fired traps without anything in them with this approach and best of all, the chucks are caught right behind the head resulting in quick death and zero to little struggle which allows for a quick reset to take the next one.
Regardless of the method, make sure to check your local laws for what's legal. Currently, in Ohio we can use 160's or 220's for chucks, but we have to have screening placed around/over the hole to prevent non targets from getting caught. However, since we have a 5" body grip on land restriction we can use 120's or 155's without the screening. That means we can catch them either going or coming thus doubling our chances of a capture.
