Ring up yer maun Fred Dibnah and see if he'll come over and take the stack down for you, then get someone to rebuild it exactly as it was.
Seriously though...
You may need to have the chimney taken down or you may get by with simply re-pointing.
Its time consuming work and probably not well paid from a builders point of view.
These days there are a whole raft of health and safety issues about working on heights etc. and you'll probably need scaffolding.
Check with your local Council in case there are planning and building regulations issues.
Use this opportunity to check for a tray flashing at the base of the chimney and consider installing one if not.
Install a proper coping if this is an area of high exposure and ensure that render is weatherproof.
If this is a brick chimney and not render you're in a whole different league.
Done correctly they can look great, but done badly - ewwww!
HTH
ONQ.