Cut the chicken into ¾-inch pieces. In a Dutch oven heat olive oil over medium-high heat. Cook and stir chicken and garlic in hot oil for 5 to 6 minutes or until chicken is no longer pink. Stir in chicken broth, mushrooms, water, carrots, kale (if using), and tarragon.
Bring mixture to boiling; reduce heat. Simmer, covered, for 2 minutes. Add tortellini. Simmer, covered, for 5 to 6 minutes more or until tortellini is tender. Stir in the spinach (if using).