Add the broth, chick peas, corn, tomatoes, onion, garlic, Italian seasoning, salt, chili powder, and cumin to the slow cooker and mix together. Place chicken pieces in the soup mixture. (You will be shredding the chicken after it cooks, so do not worry about chopping the large chicken breasts.)
Cook soup in slow cooker for 4 hours on HIGH or for 6-8 hours on LOW.
Carefully transfer chicken breasts to a plate and use two forks to shred the chicken. Set aside.
Whisk the cream cheese and pesto sauce in with the soup. Carefully add the chicken back in with the soup. Mix and allow the soup to cook on LOW for 10-15 minutes, allowing the cream cheese to melt in the soup. Mix together one last time before serving.