Preheat the oven to 350 degrees F.
Place the chicken breasts on a sheet pan and rub with the skin with olive oil. Sprinkle liberally with salt and pepper. Roast for 35 to 40 minutes, until the chicken is just cooked. Set aside until cool enough to handle. Remove the meat from the bones, discard the skin, and shred the chicken in large bite-sized pieces.
Blanch the asparagus in a pot of boiling salted water for 3 to 5 minutes until crisp-tender. Plunge into ice water to stop the cooking. Drain. Cut the peppers in strips about the size of the asparagus pieces. Combine the cut chicken, asparagus, and peppers in a large bowl.
Whisk together all of the ingredients for the dressing and pour over the chicken and vegetables. Add the scallions and sesame seeds and season to taste. Serve cold or at room temperature.
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