The State Department of Natural Resources that regulates public hunting in Hawaii has been experimenting the past couple of years with peafowl hunts. I've not done it yet, since it's only in a few select areas.

From the guys I've talked to they hunt them like turkeys, with calls (the recomended goose calls...), calling them in a then shooting them.

While upland bird hunting I there was one in thick brush but it proved impossible to get him to flush and he avoided me. I'm quite curious to try again. I heard him, but never managed to see him.