Hi George The solution that Mark suggests is one of several that employ sinking a piling into the ground next to a weight bearing footing, and then lifting the footing to bear on the piling. It is the only permanent fix, other than taking the chimney down and digging new footings. The problem comes from pouring a footing on ground that was not compacted correctly. I don't recall the names of the two other systems I've read about, but they are in back issues (approximately 12 - 16 months ago) of Fine Homebuilding. They both involved running a 12 to 16" auger into the ground until undisturbed soil base is contacted, and then raising the footings to rest on this.
BTW, a chimney should never be attached to your wooden building structure. If it were, it would be pulling your house over right now :-(