Rim sprocket usually lasts long time if the drive links on the chain are not worn and the CHAINS drive links have to be the correct pitch to MATCH the rim. As Macattack hints above, their is a 3/8 pitch chain and a 3/8 Low Pro (LP) or sometimes called picco. The LP and Picco is same. If a 3/8 chain is installed on a LP drive and roller tip LP bar things will get rough/worn fast.
I've never seen a rim sprocket on them type saws, they are usually spur type where the spur is made onto the drum.
You might try this on yours: The rim will usually just slide off the drum. If your is stuck try a gentle pry.
Look closely at the rim and see if you see any numbers stamped, then look on-line for the number and pitch. One hint that the chain and sprocket is not going to run smooth is when the chain is tensioned just snug the chain don't feel smooth using a gloved hand to pull the chain. It feels jerky. It's also a good idea to install and new rim or spur when a new chain is installed if the drive links on the old chain are worn.
I prefer the rim sprocket/drum assemblies but in your case you might have to go to a spur sprocket if things don't match. The spur type is made on the drum and usually lots cheaper than a rim at around $15
Put a little dab of grease on the shaft bushing/bearing when re-installing.
If your Craftsman 2.0 still has the exact model number would be a help to us.
Most of those saws are actually Poulans re-branded as Craftsman. Once you correctly ID one and find part numbers their are lots of parts around on fleece bay and other places.
Complete parts saws can be found reasonable also. Also keep a eye open at junk piles and yard sales. They are a OCCASIONAL use home owner saw.
Does your bar have the roller tip?????
How many Drive Links (DL) does your chain have?
Post up a close up picture of your chain showing the drive links and post any numbers that are on the rim?????????????????and maybe we can give you more information
