Heat oil in a large stockpot or Dutch oven over medium heat.
Season chicken thighs with salt and pepper, to taste.
Add chicken to the stockpot and cook until golden, about 8 -10 minutes; set chicken aside. (I wrap meat in foil to save moisture at this point)
Add coconut oil to the same stockpot over medium heat. Stir in garlic, mushrooms, onion, carrots, celery and thyme.
Cook, stirring occasionally, until tender, about 3-4 minutes.
Whisk in flour until lightly browned, about 1 minute.
Add the stock whisking constantly, until slightly thickened, about 4-5 minutes.
Roughly shred chicken with forks, then add back into the pot and add coconut milk, rosemary, sea salt and pepper to taste.
Cook on medium-low heat for an additional 15-20 minutes, covered, stirring occasionally.
Serve warm, garnished with fresh parsley and rosemary, if desired.