Alan,
I lived near Chattanooga about 25 years ago and my wife and I walked the Chicamauga, Lookout Mountain, and Missionary Ridge battlefields. I believe I have seen that Confederate trench that you are referring too. I can't remember its exact location but it was on the western slope of the mountain. There is a historic marker before you get to it and even today, this trench is readily observable on the landscape. I'm sure that the Park Rangers will have information about this area. Am looking forward to another visit!!!
Dennis