We experimented with many different ways to stop rabbits damaging (destroying completely) our plants. Chicken wire fences will work only if you dig the bottom of the fence 6-9 inches into ground keeping the fence “outside” the garden as instructed here. We have a garden almost quarter of an acre and this is not possible. In case you have a cute small garden and you want to do it, here is the instruction.
See the instruction on this nice Youtube site.