Place chicken breasts in the slow cooker. Combine tomatoes with juice, chilies, ½ cup broth, onion, garlic and cumin in a bowl. Pour mixture over chicken.
Cover; cook on low heat for 6 hours. Remove chicken from slow cooker and shred with 2 forks. Return shredded chicken to slow cooker and add another ½ cup of broth.
Cook on low for another hour.
Just before serving, add tortillas to slow cooker. Stir to blend. Serve in soup bowls, topping each serving with cheese , avocado and a squeeze of lime juice.