[linearB]

In the process of trying to diagnose a louder sound (which I now believe to be front brake related), I put my bike up on bricks and ran the engine a bit. I noticed that I was immediately able to locate a rattling sound I'd heard to the rear chain -- and watching it, you can see that the chain is visibly moving up and down a fair amount, which corresponds to the rattling sound. So, I think something is messed up there. Not knowing much about this my first two thoughts are "chain tension" or "worn teeth on the rear hub".

What steps can I take to try to isolate this a little more?

Here's some video showing the chain movement and sound. Note that the bike was on bricks on a flat surface, so all that movement is coming from the bike itself...

From the opposite side of the bike, you can really hear the clatter:
https://photos.google.com/photo/AF1QipM-8aDUYfrAd8SarrmUDQcIm8sJosy3MqRbEFHW

This is @ 120FPS and then slowed down, and shows how much the chain is moving up and down:
https://photos.app.goo.gl/DiRqUtwAkY9fkqS66

This shows the wheel moving without the engine running. It is maybe very slightly "clicky":
https://photos.app.goo.gl/g5UfgjpEmRm2u6bq5


edit: note that my snail adjusters are already in the furthest/tightest position - does that imply the chain is probably just shot, if there's this much play in it?

[no bs]

sure sounds like it!

[TomJohnston]

You say the bike is on bricks but not if the bike is on it's centerstand on the brick. If that's the case, the chain slack on the unloaded swing arm is tremendous. Before you change the adjustment, put the bike on the ground and sit on the seat. You will find the slack has decreased a lot.

[Arizoni]

With the bike sitting on the center stand, the chain should have about 1 inch of total travel when it is moved with your fingers.

If it has more than this (which I am sure it does) and your adjustment snail is already at its max limit, it's time to buy a new chain.

The chain is a #530 size with either 101 or 102 links (including the master link).

Call Tim at Baker Motorsport (Royal Enfield Ft. Worth) at 1 (817) 834-1392 and tell him about your motorcycle and ask about new chains.

Tim probably knows more about Royal Enfield parts than any one else in the world.

While your talking to him, ask him if they don't have a better chain than the OEM one from India.  Many have found those OEM chains are pretty poor excuses for a chain.

[longstrokeclassic]

If you look at the rollers you can see by the bright spots on the rollers that the sprocket is not running quite parallel to the chain. Whatever the reason, it certainly one cause of premature chain wear
Try moving one of the cams one notch to position the teeth so they run centrally  between the chain plates.
If the bike noticeably veers to the left put it back to how it was and accept it for the quality product that it is    

and it's definitely time to replace the consumables...

[johno]

The chain is rubbing, either on the chain guard or, on the engine casing.
the side plates are wearing shown by the shiny part on the sideplate, in a short period of time, the side-plates of the chain will weaken and part company and so will the chain from the bike(been there done that!)
This is due to mis-alignment, a bent chain guard and to slack chain.

[2bikebill]

Change the chain for something decent, the stock chain is poor quality.
Adjust it properly.
Check wheel alignment, but don't assume both cams should be adjusted equally. The RH cam on my bike needs to be 2 notches ahead of the left for proper wheel alignment.
Indian engineering - it's not what you'd call precision...

[Kevin Mahoney]

They also had a bad habit of chewing up rear sprockets in short order

[linearB]

Thanks for all the information, everyone. I decided that as much as I want to try to get to the bottom of this myself, I don't have the energy right now, so I dropped my bike off at the shop with new wheel bearings, sprockets, chain, brake to install and then they're going to mess around with it and look for anything else that needs fixin'. I feel a little silly because it's only a couple hours work probably, but I just have too many projects and necessary home problems to solve now (water damage to my house's exterior is a bigger problem than a noisy bike). I did visually confirm that yeah every one of those parts is worn and needs replacement; we'll see if that's the end of the list, or not.

I got all the parts from Classicmotorworks, and they shipped fast!