They will get 2 ft. tall. Saw some about that tall at James Krolls presentation this yr. Also learned that there are something like 120 different varieties of chickory and they vary tremendously in deer preference and palatability.
I had the same issue with my chicory. I called the Whitetail Institute and they were very helpful. They said to mow it down to about 8" and apply some fertilizer, both of which I did last weekend. Sure was pretty in the morning before I mowed it down, though. He said you want to do it a few weeks before you are expecting a frost.