Preheat a large skillet over medium heat. Add the oil, followed by the chopped onions, peppers, celery, and garlic. Sauté for 3-5 minutes to soften.
Pour the sautéed veggies and the drained kidney beans in a large slow cooker. Place the chicken over the top, then sprinkle the chili powder, cumin, and salt in the slow cooker.
Pour the jarred roasted red peppers and their juices in a blender. Puree until very smooth. Pour the pureed red pepper and chicken broth in the slow cooker. Cover and turn on low for 6-8 hours, or high for 3-4 hours.
When the chicken is cooked through. Remove it with tongs, and shred the chicken with a fork. Stir the shredded chicken back into the crockpot. Serve warm!
NOTE: This chili is well seasoned, but is not spicy. If you want to kick up the heat, add 1-2 teaspoons cayenne pepper. Or add hot sauce after cooking.