Season chicken breasts and roast in a 350 degree oven for approximately 30 minutes. Let cool, then chop.
Mix together chicken, scallions, red pepper, water chestnuts, pear, dijon mustard, 1 teaspoon sesame oil in a bowl and set aside. Season with ground black pepper.
In another bowl mix chopped cabbage, carrots, 2 teaspoons sesame oil, vinegar together. Season with ground black pepper.
Assemble Salad
Layer the chicken salad mixture in the bottom of your bowl, container or jar.
Next, layer the hearts of palm slices on top of the chicken mixture.
Next, layer the cabbage and carrot mixture on top of the hearts of palm.