Place the chicken breasts your slow cooker along with the salsa. Stir everything around so that the chicken is well-submerged. Place crock pot on low and cook for 4 to 6 hours, until chicken is cooked through. Transfer chicken to a cutting board and use two forks to shred it. Place shredded chicken back in the crock pot to soak up the salsa until you're ready to serve.
Add the cabbage and carrot to a mixing bowl and drizzle with lime juice and sea salt. Use your hands to massage everything together. This process will help break down some of the fibers in the cabbage so that it's softer to chew. Taste slaw for flavor and add more lime juice and/or sea salt to taste.
Add cooked brown rice to 4 bowls, followed by desired amount of slaw, shredded chicken, avocado, cilantro, and any other toppings you'd like (such as black beans, shredded cheese, sour cream, more green salsa, etc). Serve and enjoy!
*You can also use bone-in peices or boneless chicken tenders