Cut the chicken into thin strips while you heat the peanut oil in a wok or large skillet.
Add ginger and garlic and stir-fry a minute or so, stirring constantly.
Add the chicken strips and continue to stir-fry, stirring, until the chicken is done, about 5-8 minutes.
Add the soy sauce, sesame oil and sesame seeds and bring to a boil. Remove from the heat.
Assemble the wraps and serve or offer each ingredient up so everyone can make their own wraps.
Put the dipping sauces into small bowls.