Some of the state's biggest trout have been pulled from the Bighorn River. It's no wonder then that it is considered, by some, to be the best trout stream in the continental U.S. (it's got both rainbows and browns) as well as the best brown trout fishery in the world. (Of course when using such superlatives to describe any fishing area, there is always lively dispute.) The river was actually closed to fishing from 1975 to 1981 because of Native American disputes, but fishermen the country over breathed a sigh of relief when these were resolved.
So what's so special about this river? For starters, it's a tail-water fishery. That means that A, it is downstream of a dam; B, the water is cool in the summer and C, the water is ice free in the winter (this last allows for a longer growing season for the trout, which in turn allows for huge fish). And, not to get too scientific, but the surrounding limestone geology allows for large populations of mayflies and fresh water crustaceans, which happen to be excellent food sources for the fish, so there are lots of fish. Top these large numbers of large fish with a small number of anglers and you do have one of the best trout streams in the country. There are spots you can wade the river, but I recommend floating it instead.