Hi arabbadot,
I don't think you mentioned if the chainsaw was a petrol or electric one.
Anyway this may or may not be relevant. I was helping a friend today cutting a pile of logs with his electric, black and decker chainsaw and while I stood there watching, I suddenly noticed the chain went slack (never seen that before) then the chain came off and after that the chain seemed to be sticking, so we took it apart again, everything looked okay but it still kept sticking.
any way to cut to the chase, we concluded the the problem was with the gearing mechanism, behind the sprocket, under the casing.
Hope that helps.