Add the vegetables, chicken, minced garlic, broth, diced tomatoes, and seasonings into your slow cooker and stir. Cook on LOW for 6 to 7 hours OR HIGH for 4-5 hours.
Once cooking time is up, make the cornstarch slurry to thicken the stew. To a small bowl add in the water and cornstarch, then stir together until smooth.
Remove the chicken from the slow cooker and carefully shred with two forks or a meat masher. Place the shredded chicken back into the slow cooker with the cornstarch slurry and balsamic vinegar. Stir well. Cook on high for 20 minutes.