1. Saute onions in the oil for 3 minutes while you prep the garlic, carrots, and celery.
2. Add them to the pot, and saute another 3 minutes.
3. Add all ingredients to a large stockpot.
4. Bring to a brisk boil, then lower heat to low and cover.
5. Cook on low for 40 minutes, covered stirring occasionally.
6. Remove chicken carefully, shred, return to pot.