Heat oven to 350 F. In an overproof pot, heat oil to coat bottom and brown 6-8 skinless chicken thighs, in batches if necessary. Sprinkle with salt and pepper and remove from pan.
Over medium high heat add 1 stalk of sliced celery, 1-2 diced carrots and 1 diced onion. Season with salt and pepper, stirring until softened. Add 4 cloves chopped garlic, chopped mushrooms (see Note 1, below) and 4 sprigs of fresh thyme. Stir occasionally and cook for about 10 minutes, until all liquid is gone.
Add 1 cup white wine; raise heat and reduce by half. Add 2-3 cups chicken stock and bring to boil; add chicken, cover and place in oven for 2 hours. Meat will be so tender it falls right off the bone.
Remove meat from liquid. (You may stop at this point, see Note 2, below.) Pick meat from bone when cool enough to handle. Meanwhile, add 2/3 cup pitted black olives to sauce. (I like oil-cured Moroccan olives but I suggest you use olives that are not too salty which these tend to be.) Cook on stovetop until flavors have blended and sauce thickens a bit. Return meat to sauce and reheat. You can also stop at this point and reheat later.
Note 1: I like to use about 4 ounces of any exotic mushroom (such as Maitake or Oyster) except not Shiitake plus about 8 small Cremini mushrooms. I break or cut the caps of the exotics into recognizable pieces. chop up the stems finely and slice the Creminis finely. You could use button mushroom for a less expensive alternative.
Note 2: I often separate out the meat, drain off the liquid and leave it to cool in the freezer for a while so I can remove all the fat from the liquid, then resume the recipe 40-50 minutes before serving. This lets the final cooking happen just before serving.