It depends on where on the Chattooga you go. Upstream from the HWY 28 bridge for about 4 miles is delayed harvest water. Downstream from Burrell's Ford is stocked, but there are still quite a few wild fish in there. Upstream of Burrell's ford is supposed to be all wild, but some stockers make it upstream. The river used to fish much better, but lately (last 3-4 years) it has been extremely pressurized and the fishing has taken its toll. Yes, there are some huge browns and bows in there, but catching them is another thing.
There is a bunch of water to fish for trout in the upstate, but you have to do your research in order to find it. The big name rivers that you should probably start with are the Chattooga, the Chauga, the Eastatooe, and the Middle Saluda. That will get you started, but there is much more out there