Sauté the vegetables: Heat 1 tablespoon of the oil over medium-high heat in a large Dutch oven. Add both onions and cook for one minute. Add the garlic and cook for another minute. Add the carrots, peppers and celery and cook until starting to brown and soften, about 5 minutes. Stir from time to time. Remove the vegetables to a 5 quart crockpot.
Brown the chicken: Bring the Dutch oven back up to medium-high heat. Add another tablespoon of oil and brown the chicken on all sides. Remove and place in the crockpot on top of the vegetables.
Heat the liquids: Pour the wine (if using, otherwise use the extra chicken broth) into the hot Dutch oven. Scrape the browned bits from the bottom of the pot. Bring the wine to a boil and cook until it is almost evaporated (about 1-2 minutes). Add the tomatoes and chicken broth and bring to a boil. Take off the heat and cool for a few minutes.
Cook the stew: Very carefully ladle the hot liquid into the crockpot (heating the liquid will help the crock to reach a safe temperature faster). Add all remaining ingredients, including the potatoes, and close the lid. Cook on LOW for 6-8 hours or on HIGH for 4 hours.
If you like a thicker stew, you can do one of the following:
Replace half of the waxy potatoes with starchy ones
Cook the stew uncovered for the final 30 minutes of the cooking time
10 minutes before the stew is done, remove the lid and stir in a slurry of 1 tablespoon cornstarch and 2-4 tablespoons cool water. Cook without the lid until thickened.