I dealt with this in my place about 2 years ago in the south end. I believe it's required if you're making any change to furnace, etc. that vent through it (the inspector who signs off on the permit will check to make sure the chimney is lined... at least they did in my case).

I got quotes that ranged from about $4,000 to $25,000 – and in the end, we ended up spending on the high end of that, cause there was other chimney rebuild that needed to be done. It also took two companies several tries (over several weeks) to install cause the chimney had all sorts of twists and turns that they couldn't get around, so they had to open walls on each floor to help guide the liner around old (no longer used/accessible) fireplaces... so it was a bit of a nightmare. Can't get any worse, so hope yours goes more smoothly!

If I were to do it all over again, I'd ditch all the gas appliances, switch to electric hot water and a heat pump, and just cap the chimney. The world is heading that way, and it would have been far cheaper than doing the work on gas appliances and dealing with chimney lining in an old house that's naturally full of surprises once you open walls, etc.