Break the ground turkey into small pieces into a large skillet over medium heat. Add onion, cook and stir the turkey, continuing to break it into smaller pieces, until completely browned, 5 to 7 minutes. Drain as much grease as possible from the turkey.
Add tomato soup, tomatoes water, and minced garlic in a large pot; bring to a boil. Reduce heat to medium-low. Stir chickpeas, red kidney beans, carrot, chutney, curry powder, cayenne, onion powder, salt, and black pepper through the turkey mixture; bring to a simmer, place a cover on the pot, and cook until the chickpeas are tender, about 15 minutes.
Stir coconut milk through the chili, return cover to the pot, and simmer another 15 minutes.