Heat sesame oil in a large pan on medium heat. Add ground chicken and cook, breaking apart into small pieces, until chicken is no longer pink (about 5 minutes).
Add onion, carrots, celery, garlic, and ginger to chicken, and cook for 5-6 minutes more (or until onions are translucent).
Add Hoisin sauce and Soy Sauce to chicken and stir until heated throughout (about 3 minutes). Keep heat on low until ready to serve.
Scoop chicken mixture onto open lettuce leaves. Crush a handful of peanuts in a plastic bag and sprinkle atop the chicken wraps. OPTIONAL: Sprinkle wraps with a few pieces of torn cilantro and Sriracha.