In a large sauce pot or dutch oven, heat the canola oil over medium high heat. Add the celery and leeks and sauté for five minutes. Add the onions, mushrooms and ½ teaspoon of salt and and sauté for three more minutes. Add the garlic and sauté for two minutes.
Add the white wine and bring to a bubble, let simmer for three to five minutes and then add the chicken, white wine vinegar, Worcestershire sauce, chicken broth, thyme, bay leaf, salt and pepper. Bring to a boil, then cover and reduce heat.
Simmer gently for an hour. Add the carrots and potatoes and simmer for another ½ hour, or until the vegetables are tender, but not mushy. Shred the chicken into smaller pieces with two forks (it will be falling apart, so this will be really easy).