I fixed this same problem yesterday on my Homelite Super 2 Chainsaw. The method of repair is very similar to that for a lawn mower and the same replacement cord material can be used it needed. The only trick is to get a good cord tension which requires the handle to be off the cord. Remove the chainsaw side plate to get at the plastic spool the rope wraps around. Carefully remove the spool with popping out the coiled spring. Wrap the pull rope cord around the spool until only a little is left and stick the spool back in place. You may need to fidget with the spring to make the spool sit all the way down, Carefully tensing the spool about one turn and thread the end of the cord thought the cord hole in the housing. Test the tension on the cord by pulling on the cord and letting the spring pull in all the way back (Don’t let go of the end). If the tension is good, thread the handle onto the cord and knot the cord as was originally done. Bolt everything back together and you should be good to go.
Ron Gabriel, September 2006