Hi Gillylou1968,
We've got a huge Eucalyptus tree aswell, and the bark is always peeling off. It's healthy, and smells gorgeous.
I doubt very much your neighbour has poisoned it....
To be sure, and to try and save the tree if you can... check it's not subject to a Tree Preservation Order (are you in a consevation area?) and then if not, maybe get a tree surgeon to come and give qualified advice?
http://www.tree-care.info/findanarb
I do have all our trees checked tri yearly because I love them :D
Best Regards from a Tree Hugger lol
L. x