In a small bowl, combine all the sauce ingredients and whisk until blended; set aside.
In a wok over medium-high heat, add 2 tbsp. oil. When hot, working in batches, add chicken cubes; sauté until no longer pink, about 2 ½ minutes, seasoning well with salt and pepper.
Using a spider strainer, transfer to a bowl and set aside while working with the remaining chicken cubes - if it needs more oil in the wok, add 2 tbsp.
When chicken is done, transfer to the bowl. Add 1 tbsp. oil to the wok and when hot, add carrots and celery; sauté 2 ½ minutes.
To this, add broccoli florets and toss for 2 minutes before adding mixed bell peppers; sauté for 2 minutes - if the bottom of the wok gets dry, add a little more oil.
Add can of corn and can of water chestnuts; stir to coat.
Return chicken to the wok along with any accumulated juices. Pour sauce over and bring to a boil.
When it gets there, add the cornstarch mixture and stir until the sauce thickens, about 45 seconds.
Add sesame seeds and toss before serving over a bed of rice; garnish with green onions.