I used to have a lot of problems with the little monsters, especially regarding my hanging basket plants in potting soil. I take short 8"-10" long twigs and insert them into the dirt all around the pot into the soil. They have to be firmly inserted, as far as you can. This seems to deter their digging and planting acorns.
Another deterrent is my cat. She loves to chase squirrels. I don't think she has ever caught one but she keeps them on the run. I used to have problems with them eating my orchids but lately, due in large part to the cat, that seems to have stopped.
Might using the chicken wire as a "wrap" around the outside of the pot help? Of course it depends on the type of plant in question but the wrap wouldn't interefere with the growth and could be made to be easily removable.
Beverly A.