Chainsaw Repair

Jim, your piston looks toasted,  time to replace. 

The jug can probably be cleaned-up with some muriatic acid.  Apply it carefully only to the areas covered in nikasil, avoid letting it "sit" on any aluminium part of the piston.  Take your time,  clean a small area, then another, etc. to avoid letting the acid run in to the ports.

I think that your 55 has the 'more desirable' closed port cylinder, which makes it even more worth trying to save.

EDIT--As mentioned,  test it for leaks so that it doesn't get cooked again.  I have a 51 (baby brother of the 55), which is not a spectacular saw,  but I consider it to be a solid dependable saw.