Start by placing the chicken breasts in your slow cooker. Pour the green chile salsa over the top and stir to coat.
Set the slow cooker to low and cook for 4 to 6 hours until the chicken is tender.
Transfer the chicken to a cutting board, shred it with two forks, and return it to the cooker to soak in the salsa.
In a mixing bowl, combine the sliced cabbage and grated carrot. Drizzle with lime juice and sprinkle with sea salt.
Massage the slaw to soften the cabbage and enhance the flavor.
Taste the slaw and adjust the lime juice or salt as needed.
To assemble, start with a scoop of cooked brown rice in each bowl, followed by the slaw and shredded chicken.
Add sliced avocado and sprinkle with cilantro. Serve with lime wedges.