Steve,
You are right to question the chimney problem because it is not just a simple fix.
But it is not a overly complicated one once you have done foundation work.
First, get yourself a 2 or 3 man crew that works in foundation/chimney repair.
Second, you/they will need to jack up the lower side of the chimney. This is similar to raising a low spot in a pier and beam home.
I expect this will be a 2-4 pier solution, depending on the size of the base you are stabilizing. I spend $150-325 a pier for repair work on pier and beam rehab work.
Most important thing is be careful with your chimney stack. The older, the more suspect. You have to take your time when working around the base and when jacking the chimney back in place. Think '1 click and wait...then 1 click and wait.' You want a slow motion, controlled correction of the problem.
Also, have a carpenter on site when jacking the chimney back into the house. The chimney will come into contact with the house at weird angles and it may twist a little. The carpenter can help get the house and the chimney to align again.
Last thing, you personally want to be on site when any 'jacking/moving' of the chimney is going on. This will keep everyone on point and hope to insure a successful project.
Remember, it is your money, your project...so take the time and be there.
Good luck.
Kyle King