Preheat the oven to 350°F, and put a pot of salted water on high heat to cook asparagus.
NOTE: In place of the chicken breasts, I skip this step all together and just pick the meat from a whole rotisserie chicken. (Costco has the absolute best ones anywhere for only $5!) Saves time and tastes great. But, if you prefer all white meat, continue on.
Place the chicken breasts on a sheet pan and rub the skin with olive oil. Sprinkly liberally with salt and pepper. Roast for 35 to 40 minutes, until the chicken is just cooked. Set aside until cool enough to handle. (When cooled, remove the meat from the bones, discard the skin, and shred the chicken in large bite-sized pieces).
While chicken is roasting, blanch the asparagus in the pot of water for three to five minutes until crisp-tender. Plunge into ice water to stop the cooking. Drain.
Cut the pepper 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.