I am in the same position, here's what I'm doing; It's a balancing act between aesthetics/cosmetics and practicality. The old chimney will be cold, inefficient, probably damp and possibly unsound.
I am removing the chimney down to the level of the stone plinth (approx 7 feet above finished floor level), building a modern insulated (lined pumice) chimney to replace the original brick. The bricks are old, hand-made and very rustic. Because they were laid/plastered with lime they are easily reclaimed, cleaned up, and will be used to make an attractive "face" to the new chimney.
Google for Anki and Isokern chimneys to see the type of system I'm talking about.
HTH