I'm thinking of taking some extra chain and wrapping it around a tree and securing it with a 3/16 quick link. Will this be a good way to secure them? I would choose a forked tree so something couldn't climb all the way up the tree.

going after coons im assuming? if so yes lots of people chain to tress using cable, chain, or fence staple as well. Fence staples work well for coons as they are quick and easy and leave no damage to the tree.

A buddy of mine uses cable. It’s really quick and simple, but I’m not a huge fan. He uses about a 3- 6 foot Long section, so his raccoons that he catches usually wrap around other trees and get tangled up on stuff. IMO this causes pullouts and other things trappers don’t want. Usually, if it’s really wet out, the raccoons will have so much cable they can reach another tree for leverage, and can pull out. I imagine it would be a similar deal with chain. You can always try it and find out. Personally, I use cable stakes now, and try to stake them where they can’t get leverage. If they don’t have leverage, they have a lesser chance of getting out.

For example:

If your chaining to trees I'd just use cable it's much lighter and less expensive unless you have a lot of chain laying around.

If securing cable or chain to tree use big/loose loop around tree so animal can free swivel better