I strongly advise against putting the stethoscope on the moving chain!!! LOL Best of luck Boss.
I would like to suggest another way as well. If it is the chain, which I think is the most likely, a better way to find it would be to go ride the bike for 15 minutes or so to get the chain warmed up (Listening to the noise as you ride) then come back and immediately change the chain tension a good bit (looser or tighter it does not matter) and then go ride again and see if the noise changes in any way.
I suspect that it will. The noise will change, but it will not go away. If that happens then you know it is the chain.
I would for sure make sure the chain is properly adjusted. keep in mind you always have to adjust using the tightest spot in the chain, and there is always a tight spot.
I have adjusted my chain twice in the last 1000 miles or so. The chain has about 3100 miles on it. I guess I just don't understand how to find the tight point. I've tried, and it all seems the same as I spin it. Should the bike tire be on the floor while I search, or on the rear stand? Thanks for any explanation.