What if you tried tying the chicken wire to the trees instead of stapling it? I haven't done this for deer fencing but I have tied chicken wire to other kinds of fencing to keep small varmints from going under it.
Loop some plastic straw bale type or other durable twine through the fencing at top and bottom around the tree. Overlap and lace together when you get to the end of a roll. Might be stronger and it's kinder to the trees.
