Add chicken to a large pot and completely cover with water. Add Italian seasoning, bring to a simmer, and cook for 15 minutes or until the chicken is no longer pink.
Remove from water, shred, and set aside.
Chop lettuce and cabbage. Shred carrots. Add to a large mixing bowl.
Chop onions (about 1/2 cup) and cilantro; add to salad along with drained mandarin oranges, vinegar, oil, and cooled chicken; toss well to coat evenly.
Slice avocado or cut into cubes. Serve on top of each serving of salad.