Place all of the ingredients except the cilantro in a large slow cooker (4 to 6 quarts). Cook on high for 4 hours, or low for 8 hours.
Remove the chicken to a plate and shred with two forks. Use an immersion blender to blend the soup until it is mostly creamy. Return the chicken to the pot and mix well.
Serve with chopped cilantro, shredded cheese, and avocado, if desired.
