The removal of a chimney breast requires building regs approval and if a listed building or in a conservation area then P.P. also.
If the works are carried out correctly.....e.g. if any remaining part of the breast stops in the roof void then it should be supported by gallow brackets or another approved method but other than that I can't see a problem. Prior to your neighbour carrying out the works, I'd take some internal photos of the party wall in case vibration from the breast's removal causes damage to your plaster.