What should I expect when removing a chimney?
We were able to find someone to do this.  They removed part of the roof on the garage and built a ramp over the ply wood to toss down bricks.  They removed it to below the roof of the chimney and patched the hole in the roof and reinstalled the metal panels.  They also put siding on the house where the chimney was.

No mess in the living room and it was about a fifth of the price of a teardown and rebuild, approx. $2300.  This is in New England, so price might vary.  Also, the foundation for the chimney wasn't done right when built, which is why the rebuild price would have been so high.