I would guess that the Low speed mixture needle on the carburetor, the idle speed screw or both need to be adjusted. Unfortunately, the mixture needles on almost all newer carburetors are designed where the average person can't easily adjust them. You should be able to adjust the idle speed screw however. Tighten that screw a little to see if it will continue to run with a few more rpm at idle. You want the saw to idle slow enough that the chain does not move at idle.
To adjust the mixture screws, you need a special tool, or to get creative in ways you can turn those needles.
Like almost everything that is driven from Government forced regulations, these carburetors on recent small engines are pretty rediculous. Where years ago, you used to be able to adjust your own carburetor to get the engine running properly, now you have alot of engines that run marginally, have to be operated on half choke, or won't run at all due to carburetors that need to be adjusted but the average person can no longer do it. One more thing that we can blame on the liberal mindset that has taken over our country.

might try to google/utube how to adjust idle on my chainsaw or my chain saw won't idle.. see if you can find and instructional video on your problem.. agree with m21bmr adjusting low jet probably won't be easy if not impossible without spline tool or D spline tool that is if you can get the plastic lock caps off.

Some locks will let you turn them 1/16 or so either directions... Bumping the idle screw up should be straight forward. turn it in (clockwise) to raise idle.. if you adjust the low jet probably needs to go counterclockwise to richen the mixture up some. First I would try as suggested to bump idle speed up see if that helps. Chain shouldn't want to run when the saw idles. some times it will move little (depends on how tight or loose the chain is) but not continuing to running.