Season chicken breasts with salt and pepper. Grill or cook in a skillet over medium heat until fully cooked. Let cool and shred.
In a large bowl, combine napa cabbage, purple cabbage, carrots, red bell pepper, green onions, and shredded chicken.
Top with almonds, chow mein noodles, and sesame seeds if using.
Drizzle with your favorite Asian-style sesame dressing and toss to combine.
Serve immediately or refrigerate for meal prep.