Answer: I'm so sorry. Woodchucks can do terrible damage in a short time. First off you might try repairing the fence to fence it out. Wire mesh should be three to four feet tall and also buried horizontally underground, extending outward about a foot or so to deter them digging under it.
I would suggest you contact your local animal control office and see if they will remove it for you or lend you a trap, depending on your local government the policies and resources vary.
You might also contact your state game commission if you are serious about shooting it. There may be safety issues with shooting in a residential area or near a property line. You would need to be out early in the morning, around dawn or in the early evening when it is cool. They are often active during the day as well.
Please be very careful. Although they seem to become accustomed to and unfrightened by people, they are still wild. Woodchucks are wild animals -- with extremely large teeth, they can move very fast, and they are known for biting unexpectedly.
Here is some more information about woodchuck control you may find helpful.
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