chain

[capone]

how do you tighten your atv chain

[TeamCheap]

If you can post a picture of the rear axle at the swingarm we could easily help.

But in general you will have to loosen a clamp of sorts at the axle carrier and then use the chain adjusters that are there to adjust the chain tension then retorque it all down and recheck then lube the chain (if the chain is all kinked and tight/rusted lube it first before adjusting) and ride.

Some quads have adjuster bolts and some have an eccentric which is just a cylinder that has an offset hole that the axle is located in and can be spun a little to take up the chain slack.

Check your swingarm bearings for play before adjusting the chain and if OK lube the swingarm pivot bearings if you can(look for a grease zerk).
If it is loose repair it before doing anything else.