Once a chimney has moved away from the main structure it will not move back on its own. It will continue to move away from the structure until it eventually collapses. Normally a chimney can be lifted back into its original position against the house (unless debris has been trapped behind the structure such as a piece of mortar or brick).
Note* some older chimneys do not have a footing and require additional work and materials installed in order to allow a helical pier installation and lift. This is evaluated on a case-by-case basis. This piering process is exactly the same as the foundation piering procedure. Once the chimney is in its final position, any exposed gaps against the house are caulked.
We also have expert tuckpointing services available should the mortar joints need attention .