The chicken wire might help more if you lay it down on the ground. A groundhog will just burrow under a fence.
Have you tried spraying around some scent deterrents? You can make your own with garlic and eggs and such, or buy a bottle of "Critter Ridder" or some such thing and spray it on and under the plants. There's also a granular scent deterrent that may be effective - you sprinkle it on the ground. Can't recall the name but I got it at Home Depot and it has seemed to help with keeping the bunny out of the school garden.
Some people also swear by "marking the territory" by spreading your own urine around a perimeter like cats and dogs do. The groundhog may take the scent to mean there is a predator in the area and go elsewhere.
