Add all of the ingredients – except for the garnish – into a slow cooker and give the mixture a hearty stir.
Set the slow cooker to high and cook for 3 to 4 hours, or set it to low and cook for 6 to 8 hours. Cooking with high heat in less time will yield more of a soup-like consistency; whereas cooking with low heat for a longer time will create a thicker, stew-like broth.
Once the soup has cooked for about 80% of the desired cook time, remove the chicken breasts with tongs and set them on a plate. Pull the chicken apart using forks, and then place the chicken back in the slow cooker to finish cooking for the remaining time.
Serve immediately and enjoy with freshly chopped avocado, cilantro and lime juice.